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>Tc. 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<Tc. In addition, we determine the critical exponent δ=4.824(9) and several critical amplitudes from which we derive the universal amplitude ratios Rχ=1.084(18), Qc=0.431(9), Q2T=4.91(8), Q2L=1.265(24) and Uξc=1.99(1). The last result supports a relation between the longitudinal and transverse correlation functions, which was conjectured to hold below Tc but seems to be valid also at Tc.