Universality Of Ratios Research Articles

DYNAMICS OF EDEN CLUSTERS: CONFIRMATION OF APPERT–DERRIDA UNIVERSALITY

Universality of ratios of cumulants depends on the minor changes in the definition of time.

Phase transitions in (1+1)-dimensional transverse Ising models for spin S≥1/2

The phase transitions in the ground state of (1+1)-dimensional Ising models in a transverse field are studied for spin S=1/2, 1, 3/2, and 2 using the finite-size scaling method. The critical fields, thermal and correlation exponents are calculated as a function of S. The critical fields are monotonic functions of S but the exponents are S-independent and take their values for S=1/2. A novel calculational method based on universality of ratios of finite-size correlation length amplitudes is proposed and tested. It results in a much improved accuracy of extrapolation procedures. Such an universality appears to be a consequence of recently postulated conformal invariance of correlation functions of a class of two-dimensional classical models.