Comparison of symmetry breaking in the canonical and microcanonical ensembles

Alfred H�ller

Ji-Xuan Hou

Hal Tasaki

Ghofrane Bel-Hadj-Aissa, Matteo Gori

A paradigmatic example of a phase transition taking place in the absence of symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT) transition in the two-dimensional XY model. In the framework of canonical ensemble, this phase transition is defined as an infinite-order one. To the contrary, by tackling the transitional behavior of the two dimensional XY model in the microcanonical ensemble, we show that the BKT phase transition is of second order. This provides a new example of statistical ensemble inequivalence that could apply to a broad class of systems undergoing BKT phase transitions.

Carlos E. Fiore, Cláudio José DaSilva

M W Long, Peter Prelovšek, Samir El Shawish +2 more

We show how to generalize the zero-temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble which allows us to replace the involved canonical ensemble with a single appropriately chosen state; in the thermodynamic limit it provides the same physics as the canonical ensemble but with the evaluation of a single expectation value. We can employ the same system sizes as for zero temperature but, whereas the statistical fluctuations present in small systems are prohibitive, the spectra of the largest system sizes are surprisingly smooth. We investigate, as a test case, the spin conductivity of the spin-1/2 anisotropic Heisenberg model and in particular we present a comparison of spectra obtained by the canonical and microcanonical ensemble methods.