Mermin-Wagner at the crossover temperature

The Mermin-Wagner Theorem

LetA be a C∗ algebra such as the algebra of quasi-local observables of a quantum spin system on Z, and suppose {αt}t∈R is a strongly continuous one-parameter group of automorphisms of A, which we will refer to as the dynamics of the system. The examples we have in mind are the dynamics of a quantum spin system generated by a not-too-long-range interaction Φ, e.g., one that satsifies, for some λ...

Holography and the Coleman-Mermin-Wagner theorem

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. In 2 þ 1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large...

Mermin-Wagner fluctuations in 2D amorphous solids.

In a recent commentary, J. M. Kosterlitz described how D. Thouless and he got motivated to investigate melting and suprafluidity in two dimensions [Kosterlitz JM (2016) J Phys Condens Matter 28:481001]. It was due to the lack of broken translational symmetry in two dimensions-doubting the existence of 2D crystals-and the first computer simulations foretelling 2D crystals (at least in tiny syste...

Inverse Mermin-Wagner theorem for classical spin models on graphs.

In this paper we present the inversion of the Mermin-Wagner theorem on graphs, by proving the existence of spontaneous magnetization at finite temperature for classical spin models on transient on the average graphs, i.e., graphs where a random walker returns to its starting point with an average probability F<1. This result, which is here proven for models with O(n) symmetry, includes as a par...

Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases