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Both the Ising and the Heisenberg Models describe spin lattices with interaction on first neighbors. The Hamiltonian in each case is quite similar, despite the fact of treating de spins as Ising varia …

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: …

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 …

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). …

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{ …

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 …

The laws of physics are, at a fundamental level, reversible, so "mapping 2 possible states to 1 firm state" is actually imposible. This is easy to see: if you are in one of the two initial state you c …

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(\ …

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 …

After studying statistical mechanics, I understood that thermal fluctuations arise when the system of interest is in contact with a reservoir at some temperature $T$ exchanging energy. Because of this …

As you said, in any reversible transformation the system and the reservoir have the same temperature. So, since the definition of entropy needs that you take the system through a reversible path, you …

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 …

This is a rather simple question but I haven't found an answer here, I hope it's not a duplicate. Is there a model to explain the formation of a solid? In other words, Is there a way to start a model …

Also, according to the first law of thermodynamics, work done by external forces will be $dW=-P dV$. … However, energy $U$ must be still a state function, so $dW$ and $dQ$ must compensate somehow to give the first law of thermodynamics: $dU = dQ + dW$ …

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 …