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

Abstract

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 δ=4.824(9) and several critical amplitudes from which we derive the universal amplitude ratios R χ =1.084(18), Q c =0.431(9), Q 2 T =4.91(8), Q 2 L =1.265(24) and U ξ 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 .