Correlation lengths and scaling functions in the three-dimensional O(4) model

We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. From our data we calculate the scaling function of the transverse correlation length, and that of the longitudinal correlation length for T > T-C. We show that the scaling functions do not only describe the critical behaviours of the correlation lengths but encompass as well the predicted Goldstone effects, in particular the H-1/2_ dependence of the transverse correlation length for T < T-C. In addition, we determine the critical exponent delta = 4.824(9) and several critical amplitudes from which we derive the universal amplitude ratios R-x = 1.084(18), Q(C) = 0.431(9), Q(2)(T) = 4.91(8), Q(2)(L) = 1.265(24) and U-xi(C) = 1.99(1). The last result supports a relation between the longitudinal and transverse correlation functions, which was conjectured to hold below T-C but seems to be valid also at T-C. (C) 2003 Elsevier B.V. All rights reserved.