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7
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0answers
115 views
+100

Can you take the cutoff to infinity at a conformal fixed point?

A conformal fixed point is defined by $$\beta(g)=0$$ We hence know that couplings, masses and dimensions of operators do not flow in the effective Lagrangian when we change the renormalization ...
4
votes
0answers
74 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
4
votes
0answers
85 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
3
votes
0answers
54 views

Polology in Functional Integration

Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...
3
votes
0answers
118 views

Two-point correlation function for Potts Model

Consider the Potts model with three states , $\sigma (x) \in \{ 1, e^{2 \pi i/3}, e^{4 \pi i/3} \}$. I wanted to make sure that the following definition for two-point correlation function is correct: ...
3
votes
0answers
93 views

Where does one find pair-correlation functions for various materials?

What is the canonical source for finding pair-correlation functions for atoms in various materials? I am interested in both numeric computations and experimental measurements (like might be obtained ...
3
votes
0answers
1k views

How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?

I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive. The problem is to find $$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
2
votes
0answers
41 views

Non translation invariant correlator in CFT

I'm doing an exercise on vertex operators in the CFT book by Di Francesco & al.; exercise 9.2 p.329 : Using mode expansion show that: $$\langle\tilde{\phi(z)}\tilde{\phi(w)}\rangle= - \text{ln} ...
2
votes
0answers
95 views

What's the difference between correlation functions and S-matrix, and between in-in formalism (or “closed time path formalism”) and in-out formalism?

I was reading the "in-in" formalism (or "closed time path formalism" used in condensed matter physics) in cosmology created by Schwinger in 1961, and there is a saying: "they care about correlation ...
2
votes
0answers
81 views

How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
2
votes
0answers
97 views

Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
2
votes
0answers
66 views

Why does decay of correlations imply absence of order?

In a few articles I have read, a two-point correlation function $\langle g(x)g(y) \rangle$ is shown to decay with increasing distance of $x$ and $y$, and this is then taken to imply an absence of the ...
2
votes
0answers
92 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
2
votes
0answers
181 views

How does one derive the 2 halo term in two-point correlation function

This question is in reference to the paper here. In Equation (86) on page 28, the authors have given the two point correlation function \begin{equation*} \xi(\mathbf{x}-\mathbf{x}^{\prime}) = ...
1
vote
0answers
28 views

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. ...
1
vote
0answers
47 views

Physical meaning behind causal massless scalar propogator

I know that for a scalar massless field in $(3+1)$ spacetime that: $$ \langle 0 | \phi(x) \phi(y) | 0 \rangle \propto |x-y|^{-2} = (-(t_x-t_y)^2 + (\vec{x}-\vec{y})^2)^{-1}. $$ I also know that $$ ...
1
vote
0answers
22 views

Non Zero correlation function (for large separations) in one particle state?

So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function $$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\ ...
1
vote
0answers
79 views

Derivation of Higher-order correlation functions from definition

I'm trying to understand the definition of the n-th order correlation function. My aim is to translate the math into a numerical implementation in order to compute the correlation function $g^{(n)}$ ...
1
vote
0answers
178 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
0
votes
0answers
6 views

Correlation Function of Langevin Equation

Suppose $\phi(x,t)$ is a function whose dynamics are governed by a Langevin equation. We may Fourier transform to obtain a Langevin equation for $\phi(q,t)$. Is it true in general that $ \langle ...
0
votes
0answers
23 views

Correlation function and scattering amplitude in critical phenomena

When we use scattering radiation to probe critical phenomena, we have the usual Bragg relation for constructive interference $$|\vec{k}|=\frac{4\pi}{\lambda}sin\frac{\theta}{2}$$ where $\vec{k}$ is ...
0
votes
0answers
45 views

Ising Model 2D Correlation Length

I'm using Metropolis and Wolff Clustering algorithms to estimate the spin-spin correlation function $$<s_os_r>$$ I know that this is related to the correlation length but how do we determine ...
0
votes
0answers
39 views

Measuring typical distance between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. I tried to perform 2D FFT on it (using OpenCF fdt function in Python), but ...
0
votes
0answers
20 views

Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
0
votes
0answers
37 views

pair correlation function for heterogeneous nuclei

I have a system with heterogeneous size of nuclei of two liquids within a mixed fluid phase of those two liquids. I was wondering what would be the interpretation of pair correlation function for a ...