The breaking of Mermin-Wagner-Hohenberg's theorem for fractional systems

Norbert Straumann

Cezar Augusto Bonato, J. Fernando Perez, Abel Klein

Tom Griffin, Kevin T. Grosvenor, Petr Hořava +1 more

Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion ω∼k^{n} (n=2,3,…), whose naturalness is protected by polynomial shift symmetries. Here, we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.

Paul E. Lammert

Luca Salasnich

John Toner

I present a purely dynamical derivation of the Mermin–Wagner–Hohenberg theorem, and compare it with the standard equilibrium derivation. This also provides an opportunity to introduce diffusion equations and gradient expansions, both of which play a large role in what follows.