Z(4) model: Criticality and break-collapse method

Abstract

Within a real-space renormalization-group (RG) framework, we study the criticality of the Z(4) ferromagnet on the square lattice. The phase diagram (exhibiting ferromagnetic, paramagnetic, and nematiclike phase) recovers all the available exact results, and possibly is of high precision everywhere. In particular, we establish the main asymptotic behaviors (bifurcation and Ising regions). In addition, we develop an operational procedure (break-collapse method) which considerably simplifies the exact calculation of arbitrary Z(4) two-terminal clusters (commonly appearing in RG approaches).