Universal configurational structure in two-dimensional scalar models

Abstract

Monte Carlo methods are used to explore the universal configurational structure of two-dimensional spin- 1/2, spin-1 and border- phi ⁴ models. Comparison of spin- 1/2 and spin-1 data provides evidence that the magnetisation distribution (effectively the Helmholtz free-energy function) and its coupling derivative (effectively the internal-energy function) constitute readily accessible signatures of a universality class. It is shown that, when allowance is made for relatively large corrections-to-scaling effects, the behaviour of the border- phi ⁴ model may be satisfactorily matched to that of the other two models, substantiating the view that the border model does indeed belong to the Ising universality class.