Cluster Percolation and Pseudocritical Behaviour in Spin Models

Abstract

The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition, even though the system no longer shows thermal critical behaviour. We investigate the 2-dimensional Ising model and the 3-dimensional O(2) model by means of Monte Carlo simulations. We find for small fields that the line of percolation critical points has the same functional form as the line of thermal pseudocritical points.

11 pages, 7 figures, 2 tables, abstract partially changed, references added

References in corpus (1)

• A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

Cited by in corpus (10)

• Kertesz Line in the Three-Dimensional Compact U(1) Lattice Higgs Model
• The Phase Diagram of Hadronic Matter
• Field theory of Ising percolating clusters
• Cluster Percolation and Thermal Critical Behaviour
• Cluster Percolation and Explicit Symmetry Breaking in Spin Models
• Quarks and Triality in a Finite Volume
• Cluster Percolation and First Order Phase Transitions in the Potts Model
• Kertesz on Fat Graphs?
• Bound states in the 3d Ising model and implications for QCD at finite temperature and density
• Critical phenomena in disc-percolation model and its application to relativistic heavy ion collisions