Bulk and surface phase transitions in the three-dimensionalO(4)spin model

Abstract

We investigate the O(4) spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling K(c) = 0.935 856(2), and determine the bulk thermal magnetic renormalization exponents as y(t) = 1.337 5(15) and y(h) = 2.482 0(2), respectively. The universal ratio Q=m(2)(2)/m(4) is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical O(4) model with two open surfaces on which the coupling strength K(1) can be varied. At the ordinary transitions, the surface magnetic exponent is determined as y((o))(h1) = 1.020 2(12). Further, we find a so-called special surface transition at (k) = K(1)/K-1 = 1.258(20). At this point, the surface thermal exponent y(s)(t1) is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is y((s))/h1 = 1.816(2).