All Questions
Tagged with symmetry-breaking statistical-mechanics
14
questions
93
votes
3
answers
91k
views
First and second order phase transitions
Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order ...
- 34.3k
19
votes
1
answer
2k
views
Mermin-Wagner and graphene
I have been told that the Mermin-Wagner theorem disallows the existence of the crystal of graphene. However, I don't have enough knowledge to understand the Mermin-Wagner theorem. If possible can ...
- 487
10
votes
2
answers
751
views
Spontaneous symmetry breaking: proving the equivalence of two definitions
This question can be posed for both quantum and classical set-ups. For concreteness, let me consider a local, classical Hamiltonian $H$. The expectation values I consider are with respect to the usual ...
- 9,031
23
votes
3
answers
2k
views
How to rigorously argue that the superposition state is unstable in spontaneously symmetry breaking case
In quantum mechanics, the definition of symmetry breaking is nontrivial. See What is spontaneous symmetry breaking in QUANTUM systems?
Let me briefly summarize that question:
In spin-$1/2$ quantum ...
- 2,137
13
votes
5
answers
2k
views
Microcanonical ensemble, ergodicity and symmetry breaking
In a brief introduction to statistical mechanics, that is a part of a wider course on Solid State Physics I am taking, the teacher introduced the concept of microcanonical ensemble and the ergodic ...
- 1,764
8
votes
1
answer
1k
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 ...
- 26.7k
6
votes
4
answers
1k
views
If a Goldstone boson is an excitation moving between degenerate vacua, how do symmetries remain broken?
In spontaneous symmetry breaking, moving around the circular valley of the Mexican hat potential doesn’t change the potential energy. These angular excitations are called Goldstone bosons. But doesn't ...
- 26.7k
5
votes
2
answers
594
views
Why symmetry breaking?
Let me elaborate the question by using 2D Ising model without external magnetic field. When we lower the temperature and pass $T_c$ a little bit, the theory of spontaneous symmetry breaking tells us ...
- 2,311
4
votes
1
answer
582
views
How is domain wall formation related to spontaneous symmetry breaking?
It is said that domain wall formation is the signature of in spontaneous symmetry breaking but not explicit symmetry breaking. Why is this so?
- 26.7k
4
votes
1
answer
553
views
Spontaneous symmetry breaking at a finite temperature $T$: How is the state dscribed as a function of $T$?
Consider the equilibrium state of a statistical system with infinite DOF at a finite temperature $T$. For example, a Heisenberg ferromagnet with Hamiltonian $$H=-J\sum\limits_{i,j}\textbf{s}_i\cdot \...
- 26.7k
3
votes
1
answer
470
views
Nonzero spontaneous magnetization in two-dimensional Ising model
The two-dimensional Ising model with the nearest-neighbour interactions enjoys a $\mathbb{Z}_2$ symmetry under $S_i\to -S_i$; it displays sponatebous symmetry breaking at a finite temperature $T_C=2J[...
- 26.7k
3
votes
1
answer
542
views
Finite temperature spontanous symmetry breaking and Goldstone bosons
I recently asked (and then attemped to answer) a question about spontaneous symmetry breaking in the Heisenberg model:
Spontanous symmetry breaking in the Heisenberg model?
The question and then the ...
1
vote
1
answer
1k
views
Order parameter and Bose-Einstein condensation
I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization ...
0
votes
1
answer
214
views
Role of thermal fluctuations in restoring the symmetry in finite systems
A symmetry is spontaneously broken in a system with infinite number of degrees of freedom (DOF), when the system finds itself in the ground state that breaks the symmetry of the Hamiltonian. For ...
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