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In thermodynamics, the state of the system can be fully determined by knowing some thermodynamical variables. In most cases, we need three (This depends on how complex the system is). …

Here's a picture showing how different sources of noise affect the sensitivity of LIGO I'm trying to understand the frequency dependence of each curve. I'll specifically focus on seismic noise, suspe …

I obtained the Green function at finite temperature for a given system using a simulation. This means I have a list of numbers that represent G(t). Now I would like to use this information to compute …

I'm trying to solve this thermodynamics problem. … Furthermore, there are certain subtleties of thermodynamics that are confusing me. …

In many papers in Random Matrix Theory [1-3] related to quantum chaos (and, in particular, to the SYK model) they analytically continuate the partition function of the system $Z(\beta)$ into $Z(\beta …

I'm studying the SYK model and there seems two equivalent approaches for solving it. One is the diagrammatic expansion in the large $N$ limit, where we get self-consistent equations (in imaginary time …

In real time, one can calculate the two point function of a given theory using \begin{equation} G(\vec{x},t)=\langle \Omega | \phi(\vec{x},t)\phi^\dagger (0,0)|\Omega\rangle =\int_{\phi(0,0)}^{\phi(\ …

In most papers where I've read about Rindler decomposition and the Unruh effect ( see for example [1] or [2]) they start by saying that they want to find the wavefunction of the vacuum state in the ba …

I have been studying statistical field theory for a while and I still haven't found a physical explanation for this question. Every answer seems to be kind of circular. Basically something like this: …

I happened to come across the following term while doing an excercise on perturbation theory \begin{equation} H^2=J^2\sum_{<i,j>}\sum_{<k,l>}\sigma_i\ \sigma_j\ \sigma_k\ \sigma_l \end{equation} Whe …

Every answer was really useful so I will try to put it all together in one answer As Abdelmalek Abdesselam said, the partition function can we written as \begin{equation} \tag{1}\label{part} Z=\ …

The answer is that Energy and Mean Correlation are related by the following equation \begin{equation} U= -\frac{q}{2}J N <\sigma_i\sigma_j> \end{equation} where $q$ is the number of neighbours in th …

Suppose we have a classical Hamiltonian that can be divided into an “easy” part $H_0$ and a “difficult” part $\Delta H$ that depends on a parameter $g$: \begin{equation} H = H_0 + g \Delta H ~. \end{ …

The Ising model has this partition function \begin{equation} Z= \sum_{states}e^{-\beta E}= \sum_{\{\sigma \}}e^{\beta J \sum_{<i,j>}\sigma_i\sigma_j} \end{equation} The internal energy can be calcul …

Suppose I'm computing the partition function of some system -an Ising Model, for example- \begin{equation} \sum_{x_1,...,\ x_N}e^{-\beta H(x_1,...,\ x_N)} \end{equation} and I want to make a change …