# Tagged Questions

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-...

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### Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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### Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising ...
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### Criticality and the number of paths on a lattice

In the review "Scaling, universality, and renormalization: Three pillars of modern critical phenomena" by Stanley, he makes the following claim towards the end of the paper, which is neither derived ...
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### Measure of Lee-Yang zeros

Consider a statistical mechanical system (say the 1D Ising model) on a finite lattice of size $N$, and call the corresponding partition function (as a function of, say, real temperature and real ...
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### 2d Ising model in CFT and statistical mechanics

When I recently started to read about conformal field theory, one of the basic examples there is the so called Ising model. It is characterized by certain specific collection of fields on the plane ...
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### Transfer from Heisenberg to Ising model

It is well know, that ferromagnets can be described using Hamiltonian $$H = -\sum\limits_{i<j}J_{ij}\, (\mathbf{s}_i \cdot \mathbf{s}_j).$$ where (three dimensional) spins $\mathbf{s}_i$ ...
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### Thermodynamics for 1D line of 3D dipoles

The 1D Ising model was solved almost a century ago. This model assumed spins that point along the 1D line to the left or right and only considered nearest neighbors, so that the Hamiltonian with no ...
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### Books/resources for statistical field theory

I was wondering if anyone knows good, approachable textbook or other resources about statistical field theory (topics like in Kardar's Statistical physics of fields: lattice models, mean field theory, ...
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### Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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### Motivation of the Heisenberg model of ferromagnetism

In the Heisenberg model of ferromagnetism the atoms are assumed to be arranged in a lattice. The $i$-th atom has a spin operator $\vec S_i$ (here $i$ belongs to the lattice). The Hamiltonian is given ...
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### How to use Ising Spin model for prediction of time series “Phase”

I am investigating a 2d Ising Spin Lattice. I have been able to generate a Monte Carlo app that gives me the changing spin matrix through my iterations - like the many examples on the web. However, ...
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### Spontaneous symmetry breaking in the quantum 1D XX model?

The ground states of the quantum 1D Ising and Heisenberg models exhibit spontaneous magnetization. Is this also true for the 1D XX model?
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### Spin Glass Transitions in Random Bond Ising Model (RBIM)

In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its dual?...
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### Exact Solution of Ising Model in Open Boundary condition

What will be the exact expression of the partition function for 1d Ising model, if we consider open boundary case (This implies that the last spin in the sequence does not interact with the first spin)...
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### Why do the singularities of the thermodynamic functions expected to be non-negative powers?

I am going through the first chapter of Exactly Solved Models in Statistical Mechanics. On page 4, at the end of section 1.1 it is said that: I would like to know the basis of this expectation. ...
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### Master curve of the 3D Ising model

I am currently doing some grand canonical Monte Carlo simulations for LJ particles and my professor has asked me to map the normalized probability distribution of density on to a master curve of the ...
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### Intuition on Gibbs measures

I am (roughly) aware of the way Gibbs measures are used to solve physical systems (e.g. the Ising model). We can basically boil it down to pinpointing a Hamiltonian. My question is, consider a ...
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### Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
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### Majorana fermions and the continuum limit of the Ising model

In Paolo Moligini's Analyzing the two dimensional Ising model with conformal field theory lecture notes, it is shown at the end of chapter 3 that the Lagrangian of the continuum limit of the Ising ...
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### Ising model at high vs. low temperature

The output of the Ising model over a 2D binary lattice looks to have spin states uniformly distributed over the lattice for high values of the temperature parameter with the output attaining ...
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### Mixed spin Ising Model

As we know ferrimagnets can be modeled by the Ising model. I came across this equation in "Compensation Temperature of the Mixed-Spin Ising Model on the Hexagonal Lattice" by W. Figueiredo, M. Godoy, ...
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### Construction of free energy based on Landau theory

Consider an Ising model system where the total energy is $E = −J \sum_{<ij>} S_iS_j$, $S_i = \pm 1$ and $< ij >$ implies sum over nearest neighbours. For $J < 0$ the ground state of ...
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### Ising model Monte Carlo simulations in 4D and 5D

I'm going to be simulating the Ising Model in 4D and above to calculate spin-spin correlations and critical exponents and am wondering how to tackle this algorithmically. For example, in 1D, use an ...
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### Correlation time (non linear) in ising model (3D)

I am currently implementing the classical Ising model (3D) for a demonstration. I use the common implementation of metropolis,teller,teller ("Metropolis"-algorithm) and measure certain quantities. ...
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### Why doesn't the 1 dimensional ising model have a transition temperature?

Consider a 1 dimensional chain of spins that are able to either have the value $\sigma =$ $+1$, $-1$, from now on referred to as up and down. For the Hamiltonian $H = J \sum_{i,j} \sigma_i \sigma_j$ ...
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### Fluctuation-dissipation in a quantum Ising Model

For the classical Ising model, the fluctuation-dissipation theorem tells us that the Magnetic susceptibility is proportional to the variance of the magnetization. Is there an equivalent relation for ...
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### Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
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### 2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field

I have implemented the Wolff algorithm to simulate a 2D ferromagnet. It works by building a cluster of like spins and flipping them all at once to move quickly through phase space. In the case of no ...
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### Filling ising model with basis

This questions involves how to fill a lattice with ordered basis: Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...
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### Formula for the energy per site in the triangular Ising model

I'd like to check the correctness of a simulation I ran on the Ising model on a triangular by verifying if I get the good value of the mean energy per site. I found a formula giving it for high ...
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### Is this a known entropy formula?

While playing around with a variant of the one-dimensional Ising model with periodic boundary conditions I came up with a formula, let's call it $F$, whose form looks suspiciously like an entropy ...
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### Phase transition in mean field theory Ising model

For the Ising model mean field theory is supposed to give quantitatively correct answers in dimensions>=4. I have written code to compare the results of mean field theory to a 4D or 5D Ising model and ...
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### Finite Temperature Signatures of QPT in the Transverse Ising Model

We know that in the transverse ising model $H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$ there is a quantum phase transition right at the critical point $g=1$. I am wondering if ...
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### What is the motivation behind defining short range order the way it is defined in Braggs-William approximation?

I am reading Statistical Mechanics by Kerson Huang. In the chapter on Ising model, it defines short range order as $\frac{2 N^{++}}{\gamma N}$ where $N^{++}$ is total number of spin up neighbours of ...
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### Swendsen Wang different implementations

I have recently a confusion about the different adding probabilities of bonds in the Swendsen Wang cluster algorithms with e.g. application to the Ising or Potts model. In literature there are ...