The Mermin-Wagner Theorem - Condensed Matter Theory Group

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How symmetry breaking occurs in principle Actors Proof of the Mermin-Wagner Theorem Discussion It turns out that such averages may be unstable under an infinitesimal perturbation of the Hamiltonian one can define the quasi-average: Hν = H + νH ′ − µ ˆN 〈A〉 q = lim ν→0 lim V →∞ tr e −βHν A The quasi-average does not need to coincide with the normal average i C = lim q ν→0 tr e −βHν H, Γ i S = 0 − Andreas Werner The Mermin-Wagner Theorem
How symmetry breaking occurs in principle Actors Proof of the Mermin-Wagner Theorem Discussion An Example: H = − ij JijSi · Sj it is invariant under rotations in spin-space [H, S] − = 0 from S α , S β = 0 and [S − x , S y ] − = iS z we find that the conventional average of the magnetization vansihes. Adding a symmetry breaking field B0 = B0ez we may study quasi-averages and find spontaneous symmetry breaking. Andreas Werner The Mermin-Wagner Theorem
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The Mermin-Wagner Theorem - Condensed Matter Theory Group

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