# 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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### What is the probability distribution for a subsystem in canonical ensemble?

Suppose we have a 3d Ising Model(NN interaction) in simple cubic lattice, if we define a subsystem of it to be a 2d plane of spins(for example all sites with z = L/2, L being the linear system size) ...
1answer
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### How does the ground state of the quantum Ising model relate to Schrodinger equation?

The Hamiltonian $$H = -\sum_{i\in V} h_i \sigma_i^z -\sum_{(i,j)\in E} J_{ij} \sigma_i^z\sigma_j^z - \Gamma\sum_{i\in V} \sigma_i^x$$ is kind of the cost function of the quantum annealing optimization ...
1answer
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### Weird results of Monte Carlo simulation

I'm simulating the 3D Ising Model using the Wolff update algorithm. I am using the Mersenne Twister RNG. When the lattice size is $L = 50$, the specific heat curve looks very weird!! I want to ...
2answers
226 views

### APS $\eta$-invariant and spin-Ising TQFT

I am interested in the relation between the Atiyah-Patodi-Singer-$\eta$ invariant and spin topological quantum field theory. In the paper Gapped Boundary Phases of Topological Insulators via Weak ...
1answer
118 views

1answer
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### Critical Ising T transformation

How can the following be consistent? The $T$ transformation of a Virasoro character $\chi(q)$ of central charge $c$ and weight $h$ is given by $$\chi(q+1) =e^{2 \pi i (h - c/24)}\chi(q)$$ for ...
1answer
368 views

0answers
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### Transfer matrix of 1D Ising model

I'm sorry if this is trivial, I've been stuck on a definition in Yeomans, Statistical mechanics of phase transitions. In chapter five she describes the transfer matrix of the 1D Ising model with ...
1answer
89 views

### Why does the free energy depend on the configuration, in the Peierls argument?

The origin of my doubt lays on the Peierls argument to show that there is no phase transition in the 1D Ising Model. I understand that the Helmholtz Potential is the partial Lengendre transform of $U$...
0answers
231 views

### Transverse field Ising model with open boundary conditions

what is the energy dispersion of the transverse field Ising model looks like in the case of open boundary conditions? In the case of periodic boundary, the energy takes the form of and the ground ...
1answer
164 views

### Problem comparing Ising model with Mean Field Theory

After implementing the Metropolis algorithm for the Ising model, I tried comparing my values with the MFT predictions. Shouldn't the phase change occur at T/Tc? I would guess that my mistake is in ...
0answers
28 views

### Analytic methods for studying thin films (approximately 2D spin systems)

I am working on a project involving thin films of a magnetic material represented by essentially an Ising model on a 3 dimensional lattice. The bulk case is relatively straight forward, the ...
1answer
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### Understanding entanglement entropy in the transverse field Ising model

I'm working on a project studying the transverse field Ising model in 1D with periodic boundary conditions, given by $$H = - J \sum_{i=1}^{N} \sigma^z_i \sigma^z_{i+1} - h \sum_{i=1}^N \sigma^x_i$$ I ...
2answers
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### Ignoring $(\sigma_i-M)(\sigma_j-M)$ in mean field theory?

A way to do mean field theory for the Ising model is as follows. First take the Ising Hamiltonian: $$H=-J \sum_{\left<i,j\right>} \sigma_i\sigma_j$$ Let $\sigma_i=\sigma_i-M+M$ and likewise for ...
1answer
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### Will the equilibrium energy remain same for different temperatures in the 2d-Ising model?

I am doing a numerical simulation of the 2D-Ising model using the Metropolis algorithm. One of the plots that we were asked to make was Energy vs Monte-Carlo Steps for different starting Temperatures. ...
0answers
41 views

### Sums of Ising Variables

I happened to come across the following term while doing an excercise on perturbation theory H^2=J^2\sum_{<i,j>}\sum_{<k,l>}\sigma_i\ \sigma_j\ \sigma_k\ \sigma_l \end{...
1answer
32 views

### Lowest energy state possess a symmetry but Gibbs state does not?

I believe the Bose condensate to be a system where above the critical temperature the only lowest energy eigenstate breaks the U(1) symmetry but the Gibbs state does not. On the contrary; Can there ...
1answer
153 views

### Finite temperature spontanous symmetry breaking and Goldstone bosons

I recently asked (and then attemped to answer) a question about spontaneous symmetry breaking in the Heisenberg model: Spontanous symmetry breaking in the Heisenberg model? The question and then the ...
2answers
211 views

### Interpretation of Ising model simulations

I've been working on numerically solving the Ising model in a study of phase transitions, but I'm having difficulty finding material to help me discuss the results. I'm studying spontaneous ...
1answer
274 views

### Block diagonalizing a spin-chain Hamiltonian

$\newcommand{\ket}[1]{\left|#1\right>}$ I am learning about exact diagonalization methods, currently following this explanation. My question is in regards to the part where we utilize the fact ...
0answers
30 views