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Tagged with correlation-functionsising-model
34 questions
3votes
1answer
167views
Correlation function $G(x,y)$ vs Correlation length $\xi$
The correlation function, or two point function, is defined as: \begin{equation} G(x,y) = <xy> \end{equation} And the connected one is: \begin{equation} G_{C} = <xy> - <x><y> \...
- 189
5votes
1answer
106views
What information do the bootstrap equations provide for 2D CFT?
I might be missing something obvious, but reading the BPZ paper and the Ginsparg lecture notes, and based on some specific example I tried to work out, I realized I don't understand exactly what the ...
9votes
1answer
547views
Spin-Spin Correlation Function
Consider a generic magnetic system of $N$ spin; let $M(\{s_i\})=\sum_i s_i$ be the magnetization of the system. Defining the spin-spin correlation function as $$ g_{ij}=\langle s_i s_j \rangle -\...
- 133
2votes
0answers
92views
Calculating higher-order correlation functions of the Ising model
I'm trying to compute the correlation functions $<s_1...s_n>$ of specific n-spin subsets as a function of the temperature in systems with up to $N=256^2$ spins. These will be used to compute ...
0votes
0answers
37views
References on getting the correlation function in a 3D Markov Random Field?
Does anyone know where to look to find analytical formulae for the correlation function of the Ising model on a 2D or 3D lattice (assuming toroidal or infinite is easier?), or, even better, a ...
1vote
1answer
288views
Two-point-correlation in the 3D ising model
I am currently coding a 3D (Monte-Carlo) implementation of the Ising model, using the single spin-flip & Wolff algorithm. So far, I was able to calculate all the interesting observables, like $M$ ...
- 43
3votes
0answers
46views
Various types of correlation functions in models with random interactions
In the Ising model, spin correlations are characterized by the following correlation function $$ C_{ij} = \langle \sigma_i\sigma_j\rangle - \langle \sigma_i\rangle\langle \sigma_j\rangle $$ where $\...
- 6,933
0votes
1answer
83views
Correlators $\langle \psi(z_1) \cdots \psi(z_N) \sigma(w_1) \sigma(w_2) \rangle$ in Ising conformal field theory
Question: How one obtains $$\langle \psi(z_1) \cdots \psi(z_N) \sigma(w_1) \sigma(w_2) \rangle \sim \mathrm{Pf}\left( \frac{f(z_i,z_j; w_1, w_2)}{z_i-z_j}\right) \prod_{i=1}^N (z_i-w_1)^{-1/2} (z_i-...
- 1,123
4votes
1answer
229views
Duality relation for the correlation length
In this answer to my previous question, Yvan Velenik mentioned the equality for correlation lengths of dual Ising models on a square lattice $$ \xi(T) = \xi(T^*)/2. $$ I have the following questions ...
- 6,933
0votes
0answers
205views
Correlation function in the critical two-dimensional Ising model
Fifty years ago, McCoy and Wu in their book The Two-Dimensional Ising Model formulated a hypothesis about the correlation function in the critical two-dimensional Ising model. According to this ...
- 6,933
4votes
1answer
119views
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 $\mathbb{Z}^d$...
- 2,263
0votes
1answer
100views
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\...
- 909
6votes
1answer
865views
Correlations in Ising mean-field theory
I am reading the book "Critical Dynamics - A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior" (sections 1.1.2 and 1.1.3) and have been somewhat confused about the ...
- 538
0votes
1answer
193views
Ising model: How is $|\langle\sigma\rangle|^{2}=\lim _{r \rightarrow \infty} G^{(2)}(r)$?
In the book of Statistical Field Theory by Giuseppe Mussardo, on page 51, it is given while talking about Ising model that One arrives to the same conclusion by analysing the possibility of a non-...
- 2,333
5votes
0answers
884views
Decorrelation times for a 2D Ising Model over a range of temperatures
So, I'm trying to simulate the Ising Model on a 2D square lattice of spins. When exploring the auto correlation of the magnetisation: Where the auto covariance: $$A(T) = \langle(M(t)\ - \langle M\...
- 508
