# 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.

371 questions
Filter by
Sorted by
Tagged with
265 views

### Exact Correlation Function of the 2d Ising Problem

I'm working on a variation of the Ising Model for my undergraduate thesis and I need the exact correlation function of neighbouring sites $<\sigma_{1,1}\sigma_{1,2}>$ to compare with my results. ...
68 views

### References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model

I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
66 views

### Correlation functions of exactly solvable 1D quantum models

Quantum 1d spin-1/2 transverse Ising and XY models are both related to 2d classical Ising model. Are there any known simple explicit relations between correlation functions of this models? Something ...
259 views

### Can Chaos Theory be used to explain the Ising model in paramagnetic phase?

Is it possible? How can I explain the randomness of spins in the paramagnetic phase with chaos theory? In this case, is the randomness apparent? If yes, I think the temperature would be a reasonable ...
182 views

### Why entanglement entropy diverges in 2d cft?

The entanglement entropy of a region of finite length $l$ in the ground state, in 2d CFT diverges as $$S \approx \frac{c}{6} log(l)$$ (Is it c/3 or c/6 ?) Why does this diverge. In the derivation of ...
146 views

### Physical explanation of the characteristics of the order parameter of the transverse Ising Model

The Hamiltonian for transverse Ising model is $$\hat{H}=-\sum_{j=0}^{N-1}(\lambda \hat{\sigma}_j^x\hat{\sigma}_{j+1}^x+\hat{\sigma}_j^z)$$ where $\hat{\sigma}$s are Pauli matrices. This model shows ...
378 views

### Why is the critical exponent $\alpha$ negative at the Ising spin-glass transition?

The specific heat usually diverges at a phase transition - typically as a power-law, giving a critical exponent $\alpha > 0$. (Although in 2D, sometimes the divergence is only logarithmic, as with ...
409 views

### Discontinuity of free energy at phase transitions

I am learning about the two dimensional Ising model at the moment, and how it exhibits phase transitions. At the very beginning of the course we were told that: Thermodynamically, a phase ...
480 views

### What is a CFT model corresponding to a 1D transverse Ising model?

For a 1D transverse Ising model the Hamiltonian can be expressed as $$H = -J \sum_{i} S_{i}^{x}S_{i+1}^{x} - h \sum_{i} S_{i}^{z}$$ According to my understanding this undergoes a 2nd order phase ...
194 views

### How to derive ensemble average from partition function in lattice system? [closed]

I am considering a lattice model with $N$ sites. Each site is assigned with three possible spins. The number of these three possible spins are $N_1$, $N_2$ and $N_3$. So $N=N_1+N_2+N_3$. If I can ...
499 views

### Machine learning and Condensed Matter Physics [closed]

What is the state of art of the use of Machine Learning algorithms in Condensed Matter Physics and Phase transitioning? Is there any promising result that lead us to think this is a good way to pursue?...
166 views

179 views

### Writing the mean-field Hamiltonian of the 1d Ising model including nearest and next-nearest neighbour interactions [closed]

for an exercise I have to consider the 1d Ising model with a Hamiltonian of the form H = $-J_1 \sum_{i-1}^{N}S_{i}S_{i+1} - J_{2}\sum_{i=1}^{N}S_{i}S_{i+2}$. We assume the system has periodic ...
1k views

### Equivalence between Ising model and lattice gas model [closed]

The Ising Hamiltonian is $$H=-J \sum_{i=1}^N \sigma_i \sigma_{i+1} - H \sum_{i=1}^N \sigma_i$$ How I can show the lattice gas model Hamiltonian is equivalent to that of the Ising model?
242 views

### Transverse Ising model with longitudinal field at finite T: magnetisation, susceptibility,

In a Ising model with transversal and longitudinal fields $$H = B_x \sum_i S_x^{(i)} + B_z \sum_i S_z^{(i)} + J \sum_{\langle i,j\rangle} S_z^{(i)}S_z^{(j)}$$ if $B_z=0$, the magnetisation $M$ and ...
115 views

### Topological Quantum Computation Resources Prerequisite

I am about to start my BSc Theoretical Physics project on Topological Quantum Computation. I have studied the basics of quantum mechanics, condensed matter phys, statistical mechanics. Are there any ...
229 views

### Mean magnetization of the Ising model at the first-order transition line

Below the Currie temperature, the Ising model shows first-order phase transition if we consider the external field as the control parameter. The order parameter jumps from e.g., $-m_0$ to $m_0$. The ...
96 views

### How do WZW coset models contain perturbations?

I've been studying the coset construction. As far as I understand it, the Sugawara energy momentum tensor is a way of embedding the virasoro algebra inside the Lie algebra of your original WZW model. ...
95 views

### Peierl's Proof on Spontaneous Magnetization

How to modify Peierls proof to show that, for the Ising model on the hexagonal lattice with nearest neighbor ferromagnetic coupling $J$, at low temperatures there is a spontaneous magnetization?
98 views

### Ground State Entropy of a Ferromagnet and Antiferromagnet

Consider the ground state of a 1D Ising model. In the ferromagnetic case, if we are to have magnetisation along the z axis, then there is one possible microstate, with all spins aligned along z. ...
277 views

### Estimating the Free Energy of a Kink

In statistical mechanics, people often estimate whether or not a certain feature will occur by estimating the feature's free energy. For example, in the 1D Ising model, they want to estimate the ...
257 views

### Virasoro primary for 2D Ising model at critical point

It is well known that 2D Ising model at critical point can be described by a 2D CFT. The CFT is identical to free Majorana fermions. It has three primary operators namely The identity. The Ising ...
211 views

108 views

### Confusion on the Origin of Summation Approximations in the Mean Field Ising Model

Much of the literature on the mean field approximation to the Hamiltonian of the Ising Model seems to take the the treatment of the summations in the model as a trivial step to the full mean field ...
476 views

### Ising anyon topological order and its edge $c=1/2$ CFT

We know that conformal field theories are closely related to two-dimensional topological orders via edge-boundary correspondence. An Ising topological order can be obtained by gauging the fermion ...
977 views

### Antiferromagnetic and Ferromagnetic Ising Model on triangular lattice

Recently I heard a report about the antiferromagnetic Ising model in triangular lattice. It's interesting and I never realized that the result in triangular lattice would be so different from square ...
323 views

### Fermionic Hamiltonian: questions on Bogoliubov transformation and Hermiticity

In section 2.A.2 of Quantum Ising Phases and Transition in Transverse Ising Models by Suzuki, et. al. the authors give the following in their derivation of the Bogoliubov transformation for a ...
185 views

### What does it mean to Taylor expand free energy density “in gradients”?

I am self-studying Statistical Mechanics from J. Sethna's book Entropy, Order parameters, complexity. In one of the exercises (page 206), the Landau theory for the Ising Model is derived. Starting ...
521 views

### Partition function for 1D XY model [closed]

The Hamiltonian for 1D XY Model for $N$ Ising spins is written as, $$H=\sum_{i=1}^{N} \vec{S_i} . \vec{S_{i+1}} =\sum_{i=1}^{N} cos(\theta_i-\theta_{i+1})$$ Here we will implement periodic boundary ...
128 views

### Lee-Yang zeros, how to define activity

I'm studying Lee-Yang theorem following Volume I, Section 3.2 of Itzykson and Drouffe famous book. In doing so, I've stumbled upon a dilemma that - while almost ...
84 views

### Naive question about the physical dynamics for classical Ising model

Suppose we have a 2D Ising model in physical world, at finite temperature, the system have to obey the Boltzmann distribution: $$P(\{s_i\})=\frac{1}{Z}\exp^{-\beta E(\{s_i\})}$$ where $Z$ is the ...
203 views

2k views

### Exact solution of the 2D Ising model in an external magnetic field?

The 2D Ising model is a thoroughly studied model. One of the remarkable features of the model is that it predicts a hysteresis. However, I cannot seem to find the appropriate literature on this ...