# 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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### Spectral gap and Ising model

Consider an instance of the Ising model, with $N$ number of spins on a 2D square lattice (or any other 2D structure) wrapped into a torus to avoid boundary conditions (in other words, periodic ...
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### Is flowing with RG in 1D Ising model equivalent to changing the temperature of the system

Let us consider the easiest form of the Ising Hamiltonian: $$\beta H(s_i; J) = -J\sum_i^N s_i s_{i+1}$$ ($\beta = 1/k_BT$ so we already defined $J = \tilde{J}/k_BT$ with $\tilde{J}$ constant). ...
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### Reduced state of transverse ising model

Consider the model $$H = - \sum_{i=1}^{N} (\lambda \sigma_i^x \sigma_{i+1}^x + \sigma_z)$$ with periodic boundary conditions $\sigma_1^x=\sigma_{N+1}$. Equation 33 in this paper says the reduced ...
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### Long Range interaction in Ising Model [duplicate]

How do we apply mean Field Approximation to the following Hamiltonian of Ising Model in 1D? \begin{equation} \mathcal{H} = -\sum_{i=1}^{N}\sum_{j<i}\frac{J}{\lvert i - j \rvert ^ {\alpha}}\sigma_i \...
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### Classical Heisenberg model and variational free energy for the mean field [closed]

This is a homework question that I'm stuck on for 2 days, we are asked to analyze the mean field method for the Classical Heisenberg model using the variational free energy. The Hamiltonian is given ...
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### Infrared bound on Ising model

I'm currently trying to understand aspects of Hugo Duminil-Copin's Lectures on the Ising and Potts models on the hypercubic lattice. In section 4.3, he claims that for the Ising model in $\mathbb{Z}^d$...
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In general, the $p$-spin glass model focuses on $p$-body interactions like $$H({\boldsymbol {\sigma }})=\sum_{i_1,...,i_p} J_{i_{1},\ldots i_{p}} \sigma _{i_{1}}\cdots \sigma _{i_{p}}.}... • 31 2 votes 1 answer 85 views ### Di Francesco et al.'s CFT - additional corrections to free-energy for strip geometries on a lattice? In classical spin systems, there's a nice way to extract the central charge of the model by looking at finite-size corrections to the free energy of strips of length L and width W in the limit of ... • 1,360 1 vote 0 answers 31 views ### Status of Approach of constructing Hamiltonians from Transfer Matrix I am studying this old paper from J.B.Kogut on lattice gauge theories and spin systems [Rev. Mod. Phys. 51, 659(1979)]. This paper discusses about the way of constructing a quantum Hamiltonian using ... 1 vote 0 answers 49 views ### How does one get the uncertainties for the critical exponents in Metropolis Monte Carlo for the Ising model? I've recently learned the basics about simulating the Ising model with Metropolis Monte Carlo. In particular, I've seen how to evolve the system, compute the average magnetization, find the critical ... • 14.7k 1 vote 1 answer 49 views ### Non-translation invariant Gibbs state of the Ising model In the book "Statistical mechanics of lattice systems" by Sacha Friedli and Yvan Velenik, on page 157 we have the following theorem concerning non translation invariant Gibbs states of the ... • 570 0 votes 1 answer 61 views ### Ising model has short range correlation (Exercise in Velenik's book) I'm studying the book "Statistical mechanics of lattice systems" by Sacha Freidli and Yvan Velenik, exercise 3.15 page 109: Let \beta\geq 0 and h\in\mathbb{R}, show that \langle\cdot\... • 570 2 votes 1 answer 156 views ### How renormalization allows to describe critical point behaviour using the critical fixed point? As in the title, I am trying to understand how the critical fixed point (CFP) can be used to derive the thermodynamic singular behavior of the physical critical point (PCP). The context I have in mind ... • 803 1 vote 0 answers 82 views ### Equivalence between J = 0 and h = 0 in Ising model This is the hamiltonian for the Ising-model in one dimension$$H=-J \sum_{i=1}^N \sigma_i \sigma_{i+1}-h \sum_{i=1}^N \sigma_i$$with \sigma_i=\pm 1 and \sigma_{N+1}=\sigma_1 J is the ... 4 votes 0 answers 71 views ### Mean field theory of an Ising antiferromagnet I am calculating the free energy of an Ising antiferromagnet under the static magnetic field, and trying to get an expansion of free energy near the Neel temperature. But my calculation leads to a ... • 41 1 vote 0 answers 49 views ### Difference between two Monte-Carlo methods in Ising model I was working on a Monte-Carlo simulation of the Ising model. It seems that we have two different way to flip a single spin and I didn't quite understand the difference between them. Say we have N\... 3 votes 0 answers 67 views ### Factorization of 1d Ising model partition function If I'm studying a 1-dimensional Ising model such that \mathcal H = \sum_k J_k\sigma_k\sigma_{k+1}, where$$J_k=\begin{cases}J&k \in2\mathbb N\\2J&k\in2\mathbb N+1 \end{cases}$$can I ... • 147 0 votes 0 answers 22 views ### Compute correlation over time in Montecarlo COP (Kawasaki) Ising simulation I'm looking at phase transition in a binary alloy following quenching below the critical temperature. This model is equivalent to a conserved ordered parameter Ising model: the constant concentration ... 2 votes 0 answers 30 views ### The "overlap function" of a Z_2 gauge theory Consider a Z_2 gauge theory on a square lattice (Ising spins on edges) with classical degrees of freedom, i.e. \begin{equation} E = -\sum_{\square} \sigma_i\sigma_j\sigma_k\sigma_l \end{equation} ... • 321 0 votes 1 answer 44 views ### Invertibility of adjacency matrix of nearest neighbor Ising model In Goldenfled's lectures on phase transitions and the renormalization group exercise 3.3 . One is asked to consider nearest neighbor Ising model (as the pic) In the second problem, I let B_i=S_i ... 0 votes 1 answer 38 views ### Reference request: readable introduction to Landau theory and phase transition I am doing some self-study on Landau theory and phase transition models in physics. In particular I am looking at how to apply these ideas to opinion dynamics models. I found a really nice set of ... 1 vote 0 answers 59 views ### Transverse-field Ising model in the presence of a longitudinal field - ferromagnetic phase diagram I am wondering what is the phase diagram of the transverse-field Ising model in the presence of a longitudinal field, in particular, a one-dimensional spin-1/2 chain with ferromagnetic interactions. ... • 11 2 votes 0 answers 73 views ### CFT Description of the 2D Ising Model as both a free fermion theory and a \varphi^4 Landau theory There are numerous Stack Exchange answers that explain how to construct a free fermion CFT (c = 1/2) which describes the critical point of a 2D Ising model. However there are also sources that ... • 497 1 vote 0 answers 38 views ### Under dynamic scaling, Ising model emerge fractals, which implicate what？ In the lecture note of statistic field theory of David Tong, Fluctuations occur on all length scales, big and small. he post a link, a youtube video, which describe the Ising model in different ... • 11 0 votes 0 answers 46 views ### Local statistical model for percolation I am interested in classical statistical models with degrees of freedom with a finite configuration set on regular lattices, and Boltzmann weights depending on the configurations in a constant-size ... • 301 0 votes 0 answers 44 views ### Excitation energy in the free-fermion description of TFIM The transverse-field Ising model has a gapped phase when the field is large and a gapless phase when the field is small. In the gapped phase the gap grows linearly with the field. One of the ways to ... • 980 5 votes 1 answer 434 views ### Interpretation of Renormalization Group For the purposes of this question, I will be talking about systems in statistical mechanics (e.g the Ising Model) so I will assume the system of interest has a natural cutoff frequency \Lambda. For ... • 670 10 votes 2 answers 171 views ### Is there a known closed-form expression for the susceptibility of the 2-D Ising model at B = 0? The Onsager solution for the 2-D Ising model allows us to find (among other things) complicated expressions for the internal energy of the system (in the thermodynamic limit and in zero magnetic field)... • 43.8k 3 votes 0 answers 56 views ### Kasteleyn orientation in Dimer model Some Background: The problem of dimer configurations or perfect matching occurs naturally when a diatomic gas is adsorbed onto a crystalline substrate and was first discussed by Rushbrooke and Fowler. ... • 1,643 0 votes 0 answers 28 views ### 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 ... 0 votes 0 answers 47 views ### 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 ... 0 votes 0 answers 19 views ### 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 $\sigma_i,\sigma_i$ ...
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 ...
### 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?