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26 views

Kosterlitz-Thouless transition and renormalisation group theory

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
0
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0answers
7 views

How are drawing common tangents to get diffusion different for concave and convex phase fields?

Whenever there is a concept of diffusion involved and we need to decipher what is going to happen we tend to draw common tangent s in the phase field diagrams and decide which direction the diffusion ...
3
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1answer
64 views

Charge-Vortex Duality for Bosons

Consider a (2+1)d continuum field theory with the Minkowski action $$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$ where $\phi$ is a complex field. The theory undergoes a quantum phase ...
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0answers
25 views

What is the BKT transition in non-equilibrium systems?

There is a useful page on the BKT (or KT) transition here which describes the role of vortices in 2d equilibrium systems. I am interested in what happens in 2d non-equilibrium driven-dissipative ...
3
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1answer
120 views

How to interpret phase diagrams?

I find quite difficult to interpret phase diagrams in general, for example I see people discuss them along the following lines: Here we see the coexistence line between liquid-solid phases.. a ...
0
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1answer
73 views

Why isn't superconductivity destroyed by the Goldstone modes?

In BCS theory they break particle number conservation and show the existence of a gap, which would explain why groundstate properties stay relatively the same even for higher temperatures (until beta ...
0
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0answers
65 views

Why the correlation function of 2D classical XY model is written so?

2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and ...
6
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3answers
226 views

Non-uniqueness of the Order Parameter and its Critical Exponent

In the theory of phase transitions, an order parameter is usually defined as some quantity which distinguishes the two phases of the system by being zero in one phase, and non-zero in the other (see e....
1
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1answer
87 views

What is the order parameter of 2D generalized $XY$ model?

I'm now studying the phase transition of 2D generalized XY model. This model considered here has a mixture with ferromagnetic and nematic-like interactions, $$\mathcal{H}=-\sum_{\langle i j\rangle}\...
8
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1answer
607 views

What is so topological about topological phase transitions?

I am studying the KT-transition, which is called a topological phase transition. The phase transition is driven by vortices in a 2-D superfluid, where it is shown that at a critical temperature $T_c$ ...
3
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0answers
63 views

Gapless modes at the boundary between topological insulator and normal insulator

I am currently learning about topology in condensed matter physics. I think I understand most of how topological indeces come about and differences between Z and Z2 indeces and the symmetries that ...
0
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0answers
230 views

What is finite size scaling theory?

The question is in the title. I read some articles about it but I could not understand it completely. What does it mean when we say scaling of any system? Can you please give a brief introduction ...
1
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1answer
171 views

What is the difference between non-equilibrium and equilibrium phase transitions?

My question is about the distinction between certain kinds of phase transitions. I understand what the difference between first and second order ones are. What is the difference between non ...
2
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1answer
137 views

Why is it that all metals do not become superconductor by lowering the ambient temperature?

Aluminium becomes a superconductor at a temperature below $1.91$K. But I am quite certain that all metals do not exhibit superconductivity even when the temperature is lowered to nanokelvin or below. ...
1
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1answer
105 views

Ising Model with site-dependent magnetic field

Consider an Ising system in an external field, which is different at different sites. The Hamiltonian of the system is given by $H = -J\sum_{<i,j>}^{}s_i s_j - \sum_{i}^{} h_i s_i$ Here each ...
-1
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1answer
110 views

Long Range order in 2D Ising model

We know from the exact solutions for 2D Ising model on square lattice the long range order appears bellow critical temperature, but how does this agree with the Mermin-Wagner theorem, from which we ...
0
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0answers
31 views

What is an intuitive explanation of wave ordering vector $Q$? (Pierls Instability)

How does the wave ordering vector $Q$ order a CDW? I saw this vector while studying the following system. We have a system with $N$ sites and $N/2$ spinless fermions and system is in the fully ...
2
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0answers
52 views

Topological soliton objects in Minkowski v.s. Euclidean spacetime?

What makes the distinctions between the soliton objects in Minkowski or in Euclidean spacetime? It looks that usually, the Euclidean path integral is easier to be performed in many cases. In fact, ...
3
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2answers
210 views

Why does a vanishing energy gap indicate a phase transition?

More concretely: When looking at the Ising model in the description of Bogoliubov fermions, we get an explicit expression for the energy gap, that vanishes for a particular value of the magnetic field....
4
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0answers
41 views

Why does $[H,N]=0$ violate with superfluid phase judgement $\left<b\right>=0?$

I'm working with the standard Boson Hubbard model. It's Hamiltonian is defined in Fock space and commutes with total particle number N. $$[{{\hat H}_{BH}},\hat N] = 0$$ So I can simultaneously ...
1
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0answers
53 views

Symmetry breaking - mixed state in $T\rightarrow 0$ limit

In the quantum$^1$ system with a continuous symmetry (in the Thermodynamic limit) relating the ground states $\newcommand{\ket}[1]{\left|#1\right>}\{\ket{\theta}\} \newcommand{\bra}[1]{\left<#1\...
1
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1answer
159 views

Correlation length at low temperatures?

The correlation length gives (approximately) the distance over which a spin flip has an effect. For systems with ordered phases, at low temperatures the correlation length is then small (since a ...
1
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1answer
48 views

Difference in calculation of Ginzburg Criterion in Gaussian and Mean-Field theory?

In the past I asked this question asking about a subtlety in the Ginzburg criterion for mean field theory and the Gaussian approximation. I am now having a hard time determining in general what is ...
3
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2answers
108 views

What is the difference between the states of matter and the phases of matter?

What is the difference between the states of matter and the phases of matter? Should solid, liquid and gases be called states of matter or phases? How many states and phases are there? Different ...
2
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1answer
153 views

Ginzburg-Landau theory for first-order phase transitions?

In AlQuemist's answer to this PSE question:223892 and Thomas' recent answer to one of my questions. There is a mention of the application of the Ginzburg criterion and in general the Ginzburg-Landau ...
4
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2answers
132 views

Ginzburg Criterion - why average over the Correlation Length?

To derive the Ginzburg criterion for the upper-critical dimension the fluctuations are averaged over a volume set by the correlation length. Why is this done? i.e. why do we average over a volume in ...
0
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1answer
164 views

Does a gap closing mean an occurrence of a quantum phase transition?

If we have observed a closing of the excitation gap in the energy spectrum of a certain model, can we safely conclude that a quantum phase transition occurs?
4
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1answer
336 views

Does (spontaneous) symmetry breaking imply long-range order and vice-versa?

Crystalline solids have a long-range order (where symmetry is broken) but liquids have only a short-range order (where no symmetry is broken). Ferromagnets have a long-range magnetic order while a ...
2
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1answer
89 views

What factors affect the critical temperature of a material?

I recently started learning electricity in A level physics and came across the concept of superconductivity. I find this very intriguing due to its capabilities. My questions are: What are the ...
1
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0answers
69 views

Phase Transition in Graphene, classical or quantum approach?

Graphene is a high quality 2D crystal, which is stable at room temperature is amazing because in the 1930's Landau and Peierls showed that thermodynamics prevented 2D crystals from existing in free ...
4
votes
3answers
153 views

How come metal isn't considered a state of matter?

I know in chemistry metals are a class of elements on the periodic table, but in physics metal is more like a state of matter. All of the elements that are called metals on the periodic table are ...
2
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0answers
42 views

Relationship between the validity of mean field treatment and the strength of coupling/interaction

Mean field is a quite common treatment in studying phase transition and critical phenomena, although it neglects fluctuations. Imagine we have a Hamiltonian consists of free part and interaction part:...
2
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1answer
209 views

Physical meaning of topological invariant

What does it mean in terms of band structure when we say that any topological invariant of some system is non-zero? For example what does it mean when we say that Chern number=1 in case of IQHE? Does ...
1
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1answer
384 views

What is a CFT model corresponding to a 1D transverse Ising model?

For a 1D transverse Ising model the Hamiltonian can be expressed as $$H = -J \sum_{i} S_{i}^{x}S_{i+1}^{x} - h \sum_{i} S_{i}^{z}$$ According to my understanding this undergoes a 2nd order phase ...
5
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1answer
476 views

Machine learning and Condensed Matter Physics [closed]

What is the state of art of the use of Machine Learning algorithms in Condensed Matter Physics and Phase transitioning? Is there any promising result that lead us to think this is a good way to pursue?...
1
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1answer
67 views

Question about the degenerated ground states of a many body quantum system

The existence of degenerated ground states of a many-body quantum system is usually taken as a signature of the quantum order. I am considering the follow question: If we have a many-body quantum ...
2
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0answers
65 views

Heuristic argument for boson of Möbius graphene strip at low temperatures?

I recently was thinking of the implications of how electrons behave in the Möbius graphene strip at low temperatures. At high temperatures we know that there will be a parity symmetry of the system ...
1
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0answers
209 views

Machine Learning toric code ground states and phase transition under perturbation

I was wondering if the following is a viable method using machine learning and neural networks to get to the ground states of the toric code and also understand the phase transition in the presence of ...
4
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1answer
1k views

Ground state degeneracy: Spin vs Fermionic language

Let us first consider the Hamiltonian of well-known 1D periodic Ising model as $$ H = -\frac{1}{2} \sum_{j=1}^N \sigma^x_j \sigma^x_{j+1} + \frac{h}{2}\sum_{j=1}^N \sigma^z_j. $$ Now, in the ...
0
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1answer
368 views

How is the BE condensate different from ordinary states of matter?

The Bose-Einstein (BE) condensate is said to be a new state of matter which is fundamentally different from solid. liquid or gas. What are some of these properties which separate it from ordinary ...
0
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1answer
84 views

Can thermal fluctuations be a source spatial variation in local value of the order parameter?

Usually, textbooks point out that such spatial variations of the order parameter (or order parameter "density") can arise due to inhomogeneous external fields e.g., the local magnetization $m(\textbf{...
1
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1answer
143 views

What is an order parameter? Thermal average or spatial integral of a thermal average?

Sometimes the the order parameter is defined as the thermal average of a spatially varying field $\textbf{m}(\textbf{x})$ i.e., $\langle\textbf{m}(\textbf{x})\rangle$. Sometimes the order parameter (...
0
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1answer
408 views

Order parameter for liquid to crystalline solid transition under the broken continuous group of translation

The order parameter for liquid to crystalline solid transition is given by the Fourier transform of the density $$\tilde{\rho}(\textbf{k})=\int\rho(\textbf{r})e^{i\textbf{k}\cdot\textbf{r}}d^3\textbf{...
2
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1answer
209 views

What is the universal definition of the order parameter that is valid irrespective of the nature of the phase transition?

Plausible definition Consider a phase transition from phase 1 to phase 2. The order parameter is zero in one of the phases 1 or 2 and nonzero in the other. For example, in normal (phase 1) to ...
13
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3answers
749 views

Are the first order phase transitions always associated with a latent heat?

Is the first order ferromagnetic transition below the critical temperature associated with latent heat? For example, the transition of ferromagnetic configuration with all its spins aligned up to a ...
1
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1answer
314 views

Isn't the transition at the critical point always a continuous phase transition?

At page 145 of Chaikin and Lubensky's Principles of Condensed matter physics, there are two figures 4.0.1(a) and 4.0.1(b). Figure (a) shows that at $T=T_c$, there is a continuous transition (the order ...
0
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1answer
467 views

Do solids, liquids and gases resist compression due to the same reason?

In crystalline solids, the constituent atoms sit close to each other in their equilibrium positions. The solid is not compressible because as the pressure is increased, the atomic orbitals tend to ...
3
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1answer
244 views

What is the meaning of “Deconfined Quantum Critical Point”?

I tried to google it but couldn't found an intuitive explanation (not existing in Wikipedia). I have also tried to read the Science paper by T. Senthil et al, but couldn't fully understand the ...
5
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1answer
519 views

Difference between Charge Density Wave (CDW) and Superconductivity?

I am struggling to see the difference between these two mechanisms. If they are both electron-phonon mediated and both distort the lattice then why don't Cooper pairs form at the CDW transition ...
4
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2answers
482 views

Landau Theory of Phase Transitions

As often stated in books, near a phase transition we may express the free energy density as a power series in the order parameter $\phi(\mathbf{r})$. Up to quartic contributions, we have $$f=f_{0}-h\...