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Results tagged with statistical-mechanics
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user 169288
The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.
6
votes
2
answers
576
views
Why is classical spin the spin-$\infty$ representation of $SO(3)$, not the spin-$1$ represen...
Given a classical spin model,
$$H=\mathbf{S}_1\cdot \mathbf{S}_2\tag{1}$$
where $\mathbf{S}_i=(\sin\theta_i \cos\phi_i,\sin\theta_i \sin\phi_i,\cos\theta_i), i=1,2$ is the classical spin.
Given a qu …
- 2,157
6
votes
1
answer
493
views
Condensed Matter or High Energy examples in which higher-loop $n\ge 2$ correction can have i...
In QFT for high energy or condensed matter, tree level diagram means classical result or mean field. Loop diagram means quantum correction or (thermal or quantum) fluctuation above mean field. In most …
- 2,157
10
votes
1
answer
1k
views
Why does Josephson's identity $d\nu=2-\alpha$ only hold for mean field theory in dimension $4$?
For phase transition, when approaching the critical point, the heat capacity $C \propto \tau^{-\alpha}$ and correlation length $\xi\propto \tau^{-\nu}$, with $\tau := \frac{T-T_\mathrm{c}}{T_\mathrm{c …
- 2,157
23
votes
3
answers
2k
views
How to rigorously argue that the superposition state is unstable in spontaneously symmetry b...
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 …
- 2,157
35
votes
1
answer
4k
views
What's the relation between Wilson Renormalization Group (RG) in Statistical Mechanics and Q...
What's the relation between Wilson Renormalization Group(RG) in Statistical Mechanics and QFT RG? For easier to compare, I choose scalar $\phi^4$ in both cases.
Wilson RG:
Given $\phi^4$ model,
$$Z …
- 2,157