fix latex in readme

README.md

@@ -5,7 +5,7 @@
 
 A fully-connected ferromagnetic [Ising model](https://en.wikipedia.org/wiki/Ising_model) with uniform coupling strength, described by a Boltzmann distribution
 
-$$p(\boldsymbol{\sigma}) = \frac{1}{Z} \exp\left[\beta\left(\frac{J}{N}\sum_{i<j}\sigma_i\sigma_j+\sum_{i=1}^Nh_i\sigma_i\right)\right],\quad \boldsymbol{\sigma}\in\{-1,1\}^N $$
+$p(\boldsymbol{\sigma}) = \frac{1}{Z} \exp\left[\beta\left(\frac{J}{N}\sum_{i<j}\sigma_i\sigma_j+\sum_{i=1}^Nh_i\sigma_i\right)\right],\quad \boldsymbol{\sigma}\in\{-1,1\}^N $
 
 is exactly solvable in polynomial time.
 
@@ -15,8 +15,8 @@ is exactly solvable in polynomial time.
 | Normalization | $Z=\sum\limits_{\boldsymbol{\sigma}}\exp\left[\beta\left(\frac{J}{N}\sum_{i<j}\sigma_i\sigma_j+\sum_{i=1}^Nh_i\sigma_i\right)\right]$ | $\mathcal O (N^2)$ |
 | Free energy | $F = -\frac{1}{\beta}\log Z$ | $\mathcal O (N^2)$ |
 | Sample a configuration | $\boldsymbol{\sigma} \sim p(\boldsymbol{\sigma})$ | $\mathcal O (N^2)$ |
-| Average energy | $\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\left[-\left(\frac{J}{N}\sum_{i<j}\sigma_i\sigma_j+\sum_{i=1}^Nh_i\sigma_i\right)\right]$ | $\mathcal O (N^2)$ |
-| Entropy | $-\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\log p(\boldsymbol{\sigma})$ | $\mathcal O (N^2)$ |
+| Average energy | $U = \sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\left[-\left(\frac{J}{N}\sum_{i<j}\sigma_i\sigma_j+\sum_{i=1}^Nh_i\sigma_i\right)\right]$ | $\mathcal O (N^2)$ |
+| Entropy | $S = -\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\log p(\boldsymbol{\sigma})$ | $\mathcal O (N^2)$ |
 | Distribution of the sum of the N spins | $p_S(s)=\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\delta\left(s-\sum_{i=1}^N\sigma_i\right)$ | $\mathcal O (N^2)$ |
 | Site magnetizations     | $m_i=\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\sigma_i,\quad\forall i\in\{1,2,\ldots,N\}$ | $\mathcal O (N^3)$ |
 | Correlations     | $r_{ij}=\sum\limits_{\boldsymbol{\sigma}}p(\boldsymbol{\sigma})\sigma_i\sigma_j,\quad\forall j\in\{1,2,\ldots,N\},i<j$ | $\mathcal O (N^5)$ |