The Critical Behaviour of Potts Models with Symmetry Breaking Fields
نویسنده
چکیده
The Q-state Potts model in two dimensions in the presence of external magnetic fields is studied. For general Q ≥ 3 special choices of these magnetic fields produce effective models with smaller Z(Q) symmetry (Q < Q). The phase diagram of these models and their critical behaviour are explored by conventional finite-size scaling and conformal invariance. The possibility of multicritical behavior, for finite values of the symmetry breaking fields, in the cases where Q > 4 is also analysed. Our results indicate that for effective models with Z(Q) symmetry (Q ≤ 4) the multicritical point occurs at zero field. This last result is also corroborated by Monte Carlo simulations.
منابع مشابه
Cluster Percolation and Explicit Symmetry Breaking in Spin Models ∗
Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n), etc., can be equivalently described as a percolation transition of clusters. We study here the behaviour of such clusters when the presence of an external fi...
متن کاملRobust Phase Transitions for Heisenberg and Other Models on General Trees
We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d–dimensional unit sphere and the interactions are proportional to the cosines of the angles between neighboring spins. The phenomenon of interest here is the classification of phase transition (non-uniqueness of the Gibbs state) acco...
متن کاملConfinement in the q - state Potts field theory
The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for...
متن کاملGround-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension
The ground-state fidelity per lattice site is computed for the quantum threestate Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity...
متن کاملar X iv : 0 70 6 . 10 20 v 1 [ he p - th ] 7 J un 2 00 7 Confinement in the q - state Potts field theory
The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for...
متن کامل