Update documentation

_sources/book/projects/project4.md

@@ -118,6 +118,11 @@ Assume a $2 \times 2$ lattice with periodic boundary conditions.
   - total magnetisation
   - degeneracy
 
+```{note}
+When computing the energy, we have said that the sum should avoid double-counting spin pairs. However, a $2 \times 2$ lattice is a special case, since using periodic boundary conditions in this case necessarily leads to counting all spin pairs twice. So for this particular case it is OK to double-count. And we recommend doing it, since in Problem 4 we will use the analytical results from this problem to test our code, so it's useful to have the periodic boundary conditions work the same way in the $2 \times 2$ case as in the general $L \times L$ case. (Otherwise we would have to add a special `if-else` block in the code to turn off the periodic boundaries for the case when L=2.)
+```
+
+
 - **b)** Find analytical expressions for 
   - $Z$
   - $\langle \epsilon \rangle$
@@ -248,6 +253,11 @@ Time to actually write some code!
 
 **b)** Validation: For a temperature of $T = 1.0\,J/k_B$, compare your results to the analytical results from Problem 1. (Feel free to compare for other temperature values as well, or simply make plots of these quantities versus temperature.)
 
+```{note}
+See the note in Problem 1 about periodic boundary conditions for the special case of a $2 \times 2$ lattice. Short summary: it is OK to double-count spin pairs for this special case, so we can use the exact same code for all lattice sizes, including $2 \times 2$.
+```
+
+
 **c)** How many **Monte Carlo cycles** do you need to get good agreement with the analytical result? (Here *one Monte Carlo cycle* corresponds to *$N$ attempted spin flips*.)
 
 

_sources/lecture_notes/2024/README.md

@@ -181,13 +181,31 @@
 - Markov chains
 
 
-### Plan for Lecture 21, October 31:
+### Lecture 21, October 31:
 
 - Wrap up discussion of Markov chains
 - Markov chain Monte Carlo (MCMC)
-- Start on parallel computing
 
 
+### Lecture 22, November 1:
+- Wrap up discussion of MCMC
+  - MCMC code examples
+- Parallel computing
+
+
+### Lecture 23, November 7:
+- Wrap up discussion of parallel computing
+  - Amdahl's law
+- Random number generation
+- If time: start on sampling from low-dimensional pdfs
+
+
+### Lecture 24, November 8:
+- Sampling from low-dimensional pdfs
+  - Rejection sampling
+  - Importance sampling
+  - Inverse transform sampling
+
 
 
 

book/projects/project4.html

@@ -844,15 +844,21 @@ <h2>Problems<a class="headerlink" href="#problems" title="Permalink to this head
 <section id="problem-1">
 <h3>Problem 1<a class="headerlink" href="#problem-1" title="Permalink to this headline">#</a></h3>
 <p>Assume a <span class="math notranslate nohighlight">\(2 \times 2\)</span> lattice with periodic boundary conditions.</p>
-<ul>
-<li><p><strong>a)</strong> Summarise all possible states of the system by setting up a table with four coloumns showing the following quantities</p>
 <ul class="simple">
+<li><p><strong>a)</strong> Summarise all possible states of the system by setting up a table with four coloumns showing the following quantities</p>
+<ul>
 <li><p>number of spins in state +1</p></li>
 <li><p>total energy</p></li>
 <li><p>total magnetisation</p></li>
 <li><p>degeneracy</p></li>
 </ul>
 </li>
+</ul>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>When computing the energy, we have said that the sum should avoid double-counting spin pairs. However, a <span class="math notranslate nohighlight">\(2 \times 2\)</span> lattice is a special case, since using periodic boundary conditions in this case necessarily leads to counting all spin pairs twice. So for this particular case it is OK to double-count. And we recommend doing it, since in Problem 4 we will use the analytical results from this problem to test our code, so it’s useful to have the periodic boundary conditions work the same way in the <span class="math notranslate nohighlight">\(2 \times 2\)</span> case as in the general <span class="math notranslate nohighlight">\(L \times L\)</span> case. (Otherwise we would have to add a special <code class="docutils literal notranslate"><span class="pre">if-else</span></code> block in the code to turn off the periodic boundaries for the case when L=2.)</p>
+</div>
+<ul>
 <li><p><strong>b)</strong> Find analytical expressions for</p>
 <ul class="simple">
 <li><p><span class="math notranslate nohighlight">\(Z\)</span></p></li>
@@ -973,6 +979,10 @@ <h3>Problem 4<a class="headerlink" href="#problem-4" title="Permalink to this he
 <li><p><span class="math notranslate nohighlight">\(\chi / N\)</span></p></li>
 </ul>
 <p><strong>b)</strong> Validation: For a temperature of <span class="math notranslate nohighlight">\(T = 1.0\,J/k_B\)</span>, compare your results to the analytical results from Problem 1. (Feel free to compare for other temperature values as well, or simply make plots of these quantities versus temperature.)</p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>See the note in Problem 1 about periodic boundary conditions for the special case of a <span class="math notranslate nohighlight">\(2 \times 2\)</span> lattice. Short summary: it is OK to double-count spin pairs for this special case, so we can use the exact same code for all lattice sizes, including <span class="math notranslate nohighlight">\(2 \times 2\)</span>.</p>
+</div>
 <p><strong>c)</strong> How many <strong>Monte Carlo cycles</strong> do you need to get good agreement with the analytical result? (Here <em>one Monte Carlo cycle</em> corresponds to <em><span class="math notranslate nohighlight">\(N\)</span> attempted spin flips</em>.)</p>
 </section>
 <section id="problem-5">

lecture_notes/2024/README.html

@@ -663,8 +663,23 @@ <h1 class="site-logo" id="site-title">FYS3150/FYS4150 course material</h1>
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plan-for-lecture-21-october-31">
-   Plan for Lecture 21, October 31:
+  <a class="reference internal nav-link" href="#lecture-21-october-31">
+   Lecture 21, October 31:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-22-november-1">
+   Lecture 22, November 1:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-23-november-7">
+   Lecture 23, November 7:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-24-november-8">
+   Lecture 24, November 8:
   </a>
  </li>
 </ul>
@@ -782,8 +797,23 @@ <h2> Contents </h2>
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plan-for-lecture-21-october-31">
-   Plan for Lecture 21, October 31:
+  <a class="reference internal nav-link" href="#lecture-21-october-31">
+   Lecture 21, October 31:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-22-november-1">
+   Lecture 22, November 1:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-23-november-7">
+   Lecture 23, November 7:
+  </a>
+ </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-24-november-8">
+   Lecture 24, November 8:
   </a>
  </li>
 </ul>
@@ -1065,12 +1095,46 @@ <h2>Lecture 20, October 25:<a class="headerlink" href="#lecture-20-october-25" t
 <li><p>Markov chains</p></li>
 </ul>
 </section>
-<section id="plan-for-lecture-21-october-31">
-<h2>Plan for Lecture 21, October 31:<a class="headerlink" href="#plan-for-lecture-21-october-31" title="Permalink to this headline">#</a></h2>
+<section id="lecture-21-october-31">
+<h2>Lecture 21, October 31:<a class="headerlink" href="#lecture-21-october-31" title="Permalink to this headline">#</a></h2>
 <ul class="simple">
 <li><p>Wrap up discussion of Markov chains</p></li>
 <li><p>Markov chain Monte Carlo (MCMC)</p></li>
-<li><p>Start on parallel computing</p></li>
+</ul>
+</section>
+<section id="lecture-22-november-1">
+<h2>Lecture 22, November 1:<a class="headerlink" href="#lecture-22-november-1" title="Permalink to this headline">#</a></h2>
+<ul class="simple">
+<li><p>Wrap up discussion of MCMC</p>
+<ul>
+<li><p>MCMC code examples</p></li>
+</ul>
+</li>
+<li><p>Parallel computing</p></li>
+</ul>
+</section>
+<section id="lecture-23-november-7">
+<h2>Lecture 23, November 7:<a class="headerlink" href="#lecture-23-november-7" title="Permalink to this headline">#</a></h2>
+<ul class="simple">
+<li><p>Wrap up discussion of parallel computing</p>
+<ul>
+<li><p>Amdahl’s law</p></li>
+</ul>
+</li>
+<li><p>Random number generation</p></li>
+<li><p>If time: start on sampling from low-dimensional pdfs</p></li>
+</ul>
+</section>
+<section id="lecture-24-november-8">
+<h2>Lecture 24, November 8:<a class="headerlink" href="#lecture-24-november-8" title="Permalink to this headline">#</a></h2>
+<ul class="simple">
+<li><p>Sampling from low-dimensional pdfs</p>
+<ul>
+<li><p>Rejection sampling</p></li>
+<li><p>Importance sampling</p></li>
+<li><p>Inverse transform sampling</p></li>
+</ul>
+</li>
 </ul>
 </section>
 </section>