A conjecture, based on a comparison of different mean-field-like approximations, is proposed for determining the first- or second-order character of phase transitions. The q-state Potts model and several gauge theories [Z2, U(N), SU(N), SO(3)] on a lattice are considered. For Z2 gauge theory, in particular, a critical dimensionality dc=3.66 is predicted, whereas for the Potts model qc=2.75 in d=3, qc=2.4 in d=4, and qc∝exp[1/(d-1)] for d→1 are obtained.
Criterion For Distinguishing Between Continuous and Discontinuous Transitions In Spin and Gauge Systems
MARITAN, AMOS;STELLA, ATTILIO
1983
Abstract
A conjecture, based on a comparison of different mean-field-like approximations, is proposed for determining the first- or second-order character of phase transitions. The q-state Potts model and several gauge theories [Z2, U(N), SU(N), SO(3)] on a lattice are considered. For Z2 gauge theory, in particular, a critical dimensionality dc=3.66 is predicted, whereas for the Potts model qc=2.75 in d=3, qc=2.4 in d=4, and qc∝exp[1/(d-1)] for d→1 are obtained.
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