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Okay, this is a second part of my previous question. Again, I'm following Itzykson's book. The fermionic solution for the 2D Ising model is described in terms of a matrix $T = \theta \tilde{\theta}$, …

I'm currently trying to understand the physics of phase transitions and I'm having a hard time doing that. First of all, the discussions on the topic seem to be confusing and there is no methodical ap …

I was talking to a colleague professor the other day and he said something that got me curious. The way I remember it, he said basically that in experiments a Bose-Einstein condensation is usually tra …

When we study the theory of phase transitions and critical phenomena, we are taught that phase transitions are characterized by some mathematical properties. It works basically as follows. For a given …

In all textbooks I know, the derivation of the canonical probability distribution starts from the microcanonical ensemble. In my opinion, this is more of a motivation than a proper derivation, since s …

In this work, the author state that many problems in statistical mechanics center on the analysis of functional integrals of the form: \begin{equation} Z(\varphi') = \int d\mu(\varphi) e^{-V(\varphi+\ …

I think the best way to put my question is the following: what (fermionic) theories make use of Grassmann variables? Let me clarify my question a little further. I remember some discussions in quantum …

Is there a difference between renormalization and renormalization group? In his book 'Scaling and Renormalization in Statistical Mechanics', John Cardy states the following about the term Renormalizat …

In statistical field theory, one usually considers the so-called Landau Hamiltonian: $$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\ …

I'm trying to understand the discussion in this book on the fermionization of the 2D Ising model. The transfer matrix for this model becomes $T = \theta\tilde{\theta}$ where: $$\theta = e^{\beta \sum_ …

I'm learning a little bit about path integrals by myself lately and notice something quick curious. So far, I've learned that path integrals have many applications in physics, including quantum mechan …

After a very nice discussion in my previous question, I decided to move on and try to formulate the variational principle for the grand canonical ensemble. I tried following the references cited in th …

Attempted Proof: Suppose we have a family $\{f_{N}\}_{N\in \mathbb{N}}$ of functions $f_{N}: \Omega_{N} \to \mathbb{R}$. It induces a function $f: \Omega \to \mathbb{R}$ by setting $$f(x,N) := f_{N}(x …

I am a little confused about the definition of a Bose-Einstein condensate. It is said that, in such a condensate, a huge number of particles are in the same state of lower energy. The term state of lo …

In physics textbooks, one learns about Bose-Einstein condensate and it is all about taking thermodynamic limits. Of course, in real life, infinite systems do not exist. So, picture the following scena …