# 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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### How to compute correlation function and length for a given lattice configuration?

Focusing on the Ising model, for a given lattice configuration of up and down spins (say square or triangular lattice), and a given interaction type (ferromagnetic or antiferro), how can one compute ...
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### Why do fermions anti-commute in Ising model?

In my course fermions are given like a product of spin and (dual to spin) disorder parameter in 2D Ising square lattice. Then, using the properties of disorder parameter I can prove that fermions ...
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### How to get mass near the critical point for 2D Ising model on square lattice for fermions?

Let's assume that we have 2D square lattice with spins $\sigma=\pm 1$ and equal vertical and horisontal energy coefficients K: $$E_{interaction}=e^{K\sigma_i\cdot\sigma_j}$$ where $\sigma_i,\sigma_i$ ...
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### How do spin operators work? [closed]

I am currently studying statistics and 2D Ising models and noticed in my lecturer's notes the operators, acting in the spin space The text says that this is identity $2^N\times 2^N$ matrix. I don't ...
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### How does the value $k$ work in MCMC algorithm in the case of Ising model?

Here they say that $k$ is Boltzmann's constant. However, here they are saying that $k$ is a variable Can anyone explain what the catch is here?
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### What is the fundamental difference between the Ising and Potts models?

What I understand is that the only difference between the Ising and Potts models is that Ising has two types of spins, and Potts has n types of spins. However, I am wondering if the Hamiltonian (...
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### How to formulate the braiding of instanton?

I'm reading the paper https://arxiv.org/abs/2108.08835, after imposing the $\mathbb{Z}_2$ on-site symmetry, in the $J=0$ symmetric phase of the 1d Ising chain, the topological sectors of operators ...
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### What is a "transient state" and "transition state" in Ising model?

I was analyzing this source code of the Ising model. I found the term "transient state". I also found the term in this text: There are two absorbing states in this Markov chain because once ...
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### Eigenvector of ground state (GS) of spins and fermions

I'm working with the hamiltonian of XX model on a spin basis and in a fermionic basis. I have the following problem to solve: In the ground state, the number of spins up (and by convention, fermions) ...
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### Entanglement entropy of the infinite transverse field Ising chain at the critical point

Consider the $1$D transverse-field Ising model, $$H = -\sum_i \sigma_i^z \sigma_{i+1}^z-h\sum_i \sigma_{i}^x$$ at the critical point $h=1$ with periodic boundary conditions. Question: What is the (von ...
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### Reference on Curie-Weiss model

I am looking for a reference on the Curie-Weiss model and mean-field approximation. Model. Consider the Curie-Weiss model with the following Hamiltonian: \begin{align*} H = - \frac{J}{2N} \sum_{i \neq ...
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### Qubit Resource Estimates for 2D Ising Model

I recently came across this paper where the 1d Transverse Field Ising Model (TFIM) with $n$ spins was simulated on a quantum computer. The estimated resources were $n^2$ for the number of gates and ...
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### Flipping multiple spins in Ising model

I am currently working on the Ising model in 2D using the Monte Carlo simulation. What I face is that sampling physical properties such as susceptibility, magnetization, and specific heat are not ...
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### Why is the free energy unitless when taking the thermodynamic limit?

Why is the (Helmhotz) free energy unitless when taking the thermodynamic limit? Given the partition function $Z$ of a (finite size) system, the free energy is given by $F =-kT \log[Z]$, where $k$ is ...
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### How was the minimal model with a boundary related to the D brane?

Quote my advisor: The D brane was the boundary of the CFT However, in the development of the rational CFT, such as the minimal model, the D brane was not realized. Thus, when the boundary CFT was ...
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### Ising model correlation function in the high temperature limit

I'm reading the book 'Gauge Fields and Strings' by A. Polyakov and I don't understand his derivation of the correlation function of the Ising model in the high temperature limit. I don't really ...
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### How to take into account finite temperature in transverse Ising chain?

A similar question has already been asked here What I'm wondering is how to take into account finite temperature in the transverse Ising chain and see how that affects the magnetization. The reason ...
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### Meaning of 'thermalization' in Markov Chain Monte Carlo simulations

In performing MCMC simulations, it is standard practice to 'equilibriate' or 'thermalize' the system and then discard the initial data before useful sampling is done. My question is about the concept ...
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### Reference request: Kawasaki dynamics for Ising model

I want to learn more about Glauber and Kawasaki dynamics which, by my understanding, are used to model lattice spin systems for the pre-equilibrium Ising model. There seems to be quite a few ...
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### Transverse field Ising model quantum phase transition

I am looking at the quantum phase transition of the transverse field Ising model. Let: \begin{equation} H = -J \sum_{x=1}^{N-1} \sigma_x^3\sigma_{x+1}^3 - B \sum_{x=1}^N \sigma_x^1 \end{equation} Once ...
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### Ground state energy from Hamiltonian [closed]

It has been a long time since I did QM, and I am getting stuck at the most basic stuff. Assume I have a Hamiltonian: \begin{equation} H = \int_{-\pi}^\pi f(q) \left[\alpha^\dagger_q, \alpha_q \right]\...
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