build based on 97113e1

previews/PR178/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-17T18:57:27","documenter_version":"1.1.1"}}
+{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-17T20:49:27","documenter_version":"1.1.1"}}

previews/PR178/examples/fei2_classical.html

@@ -175,4 +175,4 @@
     )
 )
 Colorbar(hm.figure[1,2], hm.plot)
-hm</code></pre><img src="fei2_classical-a20d933e.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="powder_averaging.html">« Powder Averaged CoRh₂O₄</a><a class="docs-footer-nextpage" href="ising2d.html">Classical Ising model »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 18:57">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+hm</code></pre><img src="fei2_classical-a20d933e.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="powder_averaging.html">« Powder Averaged CoRh₂O₄</a><a class="docs-footer-nextpage" href="ising2d.html">Classical Ising model »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 20:49">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR178/examples/fei2_tutorial.html

@@ -156,4 +156,4 @@
 fig = Figure()
 ax = Axis(fig[1,1]; xlabel="Momentum (r.l.u.)", ylabel="Energy (meV)", xticks, xticklabelrotation=π/6)
 heatmap!(ax, 1:size(is_averaged, 1), energies, is_averaged)
-fig</code></pre><img src="fei2_tutorial-1fdd91bd.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. This is the subject of our <a href="fei2_classical.html#FeI-at-Finite-Temperature">FeI₂ at Finite Temperature</a> tutorial.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="out_of_equilibrium.html#CP-Skyrmion-Quench">CP² Skyrmion Quench</a> tutorial shows how this dynamics gives rise to the formation of novel topological defects in a temperature quench.</p><p>Relative to LSWT calculations, it can take much more time to estimate <span>$\mathcal{S}(𝐪,ω)$</span> intensities using classical dynamics simulation. See the <a href="https://nbviewer.org/github/SunnySuite/SunnyTutorials/tree/main/Tutorials/">SunnyTutorials notebooks</a> for examples of &quot;production-scale&quot; simulations.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="out_of_equilibrium.html">CP² Skyrmion Quench »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 18:57">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="fei2_tutorial-1fdd91bd.png" alt="Example block output"/><p>This result can be directly compared to experimental neutron scattering data from <a href="https://doi.org/10.1038/s41567-020-01110-1">Bai et al.</a></p><img src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/FeI2_intensity.jpg"><p>(The publication figure accidentally used a non-standard coordinate system to label the wave vectors.)</p><p>To get this agreement, the use of SU(3) coherent states is essential. In other words, we needed a theory of multi-flavored bosons. The lower band has large quadrupolar character, and arises from the strong easy-axis anisotropy of FeI₂. By setting <code>mode = :SUN</code>, the calculation captures this coupled dipole-quadrupole dynamics.</p><p>An interesting exercise is to repeat the same study, but using <code>mode = :dipole</code> instead of <code>:SUN</code>. That alternative choice would constrain the coherent state dynamics to the space of dipoles only.</p><p>The full dynamical spin structure factor (DSSF) can be retrieved as a <span>$3×3$</span> matrix with the <a href="../library.html#Sunny.dssf-Tuple{SpinWaveTheory, Any}"><code>dssf</code></a> function, for a given path of <span>$𝐪$</span>-vectors.</p><pre><code class="language-julia hljs">disp, is = dssf(swt, path);</code></pre><p>The first output <code>disp</code> is identical to that obtained from <code>dispersion</code>. The second output <code>is</code> contains a list of <span>$3×3$</span> matrix of intensities. For example, <code>is[q,n][2,3]</code> yields the <span>$(ŷ,ẑ)$</span> component of the structure factor intensity for <code>nth</code> mode at the <code>q</code>th wavevector in the <code>path</code>.</p><h2 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h2><p>The multi-boson linear spin wave theory, applied above, can be understood as the quantization of a certain generalization of the Landau-Lifshitz spin dynamics. Rather than dipoles, this dynamics takes places on the space of <a href="https://arxiv.org/abs/2106.14125">SU(<em>N</em>) coherent states</a>.</p><p>The full SU(<em>N</em>) coherent state dynamics, with appropriate quantum correction factors, can be useful to model finite temperature scattering data. In particular, it captures certain anharmonic effects due to thermal fluctuations. This is the subject of our <a href="fei2_classical.html#FeI-at-Finite-Temperature">FeI₂ at Finite Temperature</a> tutorial.</p><p>The classical dynamics is also a good starting point to study non-equilibrium phenomena. Empirical noise and damping terms can be used to model <a href="https://arxiv.org/abs/2209.01265">coupling to a thermal bath</a>. This yields a Langevin dynamics of SU(<em>N</em>) coherent states. Our <a href="out_of_equilibrium.html#CP-Skyrmion-Quench">CP² Skyrmion Quench</a> tutorial shows how this dynamics gives rise to the formation of novel topological defects in a temperature quench.</p><p>Relative to LSWT calculations, it can take much more time to estimate <span>$\mathcal{S}(𝐪,ω)$</span> intensities using classical dynamics simulation. See the <a href="https://nbviewer.org/github/SunnySuite/SunnyTutorials/tree/main/Tutorials/">SunnyTutorials notebooks</a> for examples of &quot;production-scale&quot; simulations.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="out_of_equilibrium.html">CP² Skyrmion Quench »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 20:49">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR178/examples/ising2d.html

@@ -14,4 +14,4 @@
 sampler = LocalSampler(kT=Tc, propose=propose_flip)
 for i in 1:nsweeps
     step!(sys, sampler)
-end</code></pre><p>Plot the Ising spins by extracting the <span>$z$</span>-component of the dipoles</p><pre><code class="language-julia hljs">heatmap(reshape([s.z for s in sys.dipoles], (L,L)))</code></pre><img src="ising2d-f39f34dd.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="fei2_classical.html">« FeI₂ at Finite Temperature</a><a class="docs-footer-nextpage" href="spinw/08_Kagome_AFM.html">Tutorial 8 - Kagome Antiferromagnet »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 18:57">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><p>Plot the Ising spins by extracting the <span>$z$</span>-component of the dipoles</p><pre><code class="language-julia hljs">heatmap(reshape([s.z for s in sys.dipoles], (L,L)))</code></pre><img src="ising2d-f39f34dd.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="fei2_classical.html">« FeI₂ at Finite Temperature</a><a class="docs-footer-nextpage" href="spinw/08_Kagome_AFM.html">Tutorial 8 - Kagome Antiferromagnet »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 20:49">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR178/examples/out_of_equilibrium.html

@@ -52,4 +52,4 @@
 
 plot_triangular_plaquettes(sun_berry_curvature, frames; resolution=(1800,600),
     offset_spacing=10, texts = ["\tt = "*string(τ) for τ in τs], text_offset = (0.0, 6.0)
-)</code></pre><img src="out_of_equilibrium-c31de6b4.png" alt="Example block output"/><p>The times are given in <span>$\hbar/|J_1|$</span>. The white background corresponds to a quantum paramagnetic state, where the local spin exhibits a strong quadrupole moment and little or no dipole moment. Observe that the process has generated a number of well-formed skyrmions of both positive (red) and negative (blue) charge in addition to a number of other metastable spin configurations. A full-sized version of this figure is available in <a href="https://doi.org/10.1103/PhysRevB.106.235154">Dahlbom et al.</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="fei2_tutorial.html">« Case Study: FeI₂</a><a class="docs-footer-nextpage" href="powder_averaging.html">Powder Averaged CoRh₂O₄ »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 18:57">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre><img src="out_of_equilibrium-c31de6b4.png" alt="Example block output"/><p>The times are given in <span>$\hbar/|J_1|$</span>. The white background corresponds to a quantum paramagnetic state, where the local spin exhibits a strong quadrupole moment and little or no dipole moment. Observe that the process has generated a number of well-formed skyrmions of both positive (red) and negative (blue) charge in addition to a number of other metastable spin configurations. A full-sized version of this figure is available in <a href="https://doi.org/10.1103/PhysRevB.106.235154">Dahlbom et al.</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="fei2_tutorial.html">« Case Study: FeI₂</a><a class="docs-footer-nextpage" href="powder_averaging.html">Powder Averaged CoRh₂O₄ »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.1 on <span class="colophon-date" title="Tuesday 17 October 2023 20:49">Tuesday 17 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>