# Questions tagged [ising-model]

The Ising model of ferromagnetism in statistical mechanics consists of discrete bimodal (+1 or −1) "spin" (moment) variables in a simple Hamiltonian interacting with their next neighbors on a lattice. The one-dimensional variant does not evince a phase transition, but the two-dimensional square-lattice one does. Use for analog and generalized discrete models on several lattices and dimensions.

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### Why does the Ising model at the critical point have scale invariance?

If my current understanding of phase transitions and the renormalization group (RG) method is true, RG is a kind of 'zooming out' process, since this procedure makes a block of neighboring spins and ...
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### Critical exponent $\nu$ of 3d Ising model

this question comes from an exercise of Sethna's book "Statistical Mechanics: Entropy, Order Parameters and Complexity". it is in page 282 question 12.2 In 3d Ising model, the spin ...
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### Phase transition in parameter (and not temperature) for a classical system

Consider the $q$-state Potts model on $\mathbb{Z}^d$ for some integer $q$ - this also has an FK-representation for any real number $q$. For $d = 2$ the model is exactly solvable and has a critical ...
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### Estimating the heat capacity of ising model

I am have written a Metropolis-Hastings algorithm and am currently trying to compare it to the analytical results for the 2D Ising model. The free energy seems reasonable but the heat capacity I'm ...
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### Applications of Sampling from SK Ising Model

I have written a program for Monte Carlo sampling from Sherrington-Kirkpatrick (SK) Ising model. I have two questions about it: 1- What are some applications of it? I already know training Boltzmann ...
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### Simple Quantum Monte Carlo question

Currently I am doing some simple simulation of 1D Transverse field Ising model. I map the quantum mechanical problem into classical 2D classical Ising model with different horizontal interaction and ...
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### Numerical renormalization of 2D Ising lattice

I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
The hamiltonian of a collection of noninteracting quantum spin-$1/2$ operators $\hat{S}_i$ fixed at each lattice site $i(=1,2,..., N)$ in presence of magnetic field ${\bf B}=B\hat{{\bf z}}$ $$\hat{H}=-... 2answers 53 views ### Averages of absolute values in Monte Carlo simulation of Ising Model Consider the 2D Ising model in 0 field, with Hamiltonian$$ H=J\sum_{\langle i,j\rangle}\sigma_i\sigma_j$$The magnetization per spin is defined as$$M=\frac{1}{N}\sum_i \sigma_i  Where $N$ is ...
I am want to calculate the specific heat for 2D 100x100 square lattice ising model. I have calculated the correlation time, viz., $\tau$. Now I want to calculate the specific heat and error in ...