Goldstone-mode effects and scaling function for the three-dimensional O(4) model

Abstract

We investigate numerically the three-dimensional O(4) model on 24 3 -120 3 lattices as a function of the magnetic field H. We verify explicitly the singularities induced by Goldstone modes in the low-temperature phase of the model, and show that they are also observed close to the critical temperature. Our results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The resulting expression is used to generate the magnetization's scaling function parametrically.

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

“…For the ratio R χ several alternative values exist: from the parametrization of the equation of state in [11] one gets 1.126 (9), from another parametrization in [9] 1.12 (11), from the 1/N-expansion of Oku and Okabe [25] 1.098, and from the ǫ-expansion 1.239 [12]. Our finding for Q c is well in accord with the result 0.44(2) of [9].…”

“…It also represents the data at higher magnetic fields very well. From these additional data a marginal negative correction-to-scaling term may be inferred, which is however irrelevant at low H. Compared to the corresponding fit in [11], where δ = 4.86(1), we note that our new result for δ is closer to the value 4.789(6) from Ref. [23].…”

“…As in Ref. [11] we have used the Wolff single cluster algorithm [19], which was modified to include a nonzero magnetic field [20]. In order to reduce the integrated autocorrelation time τ int we performed 100-3000 cluster updates between two measurements for H > 0, such that we obtained τ int ∼ < 3 for L = 48 and τ int ∼ < 5 for L ≥ 72.…”

“…In the same paper the amplitude B c and the critical exponent δ were determined from fits to the critical behaviour of M on the critical line. Since we have done new simulations on the critical line with higher statistics and at more H-values on the larger lattices than in [11] we could improve the analysis with the new magnetization data. …”

“…Since we have changed the values of H 0 and of δ in comparison to Ref. [11], we have redone the corresponding parametrization fits. With the new data we find…”