Monte Carlo test of critical exponents in 3D Heisenberg and Ising models

We have tested the theoretical values of critical exponents, predicted for the three–dimensional Heisenberg model, based on the published Monte Carlo (MC) simulation data for the susceptibility. Two different sets of the critical exponents have been considered – one provided by the usual (perturbative) renormalization group (RG) theory, and another predicted by grouping of Feynman diagrams in φ model (our theory). The test consists of two steps. First we determine the critical coupling by fitting the MC data to the theoretical expression, including both confluent and analytical corrections to scaling, the values of critical exponents being taken from theory. Then we use the obtained value of critical coupling to test the agreement between theory and MC data at criticality. As a result, we have found that predictions of our theory (γ = 19/14, η = 1/10, ω = 3/5) are consistent, whereas those of the perturbative RG theory (γ ≃ 1.3895, η ≃ 0.0355, ω ≃ 0.782) are inconsistent with the MC data. The seemable agreement between the RG prediction for η and MC results at criticality, reported in literature, appears due to slightly overestimated value of the critical coupling. Estimation of critical exponents of 3D Ising model from complex zeroth of the partition function is discussed. We conclude that the recent MC data can be completely explained within our theory rather than within the conventional RG theory.