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Critical exponents and equation of state of the three-dimensional Heisenberg universality class,” cond-mat/0110336

By Massimo Campostrini, Martin Hasenbusch, Andrea Pelissetto, Paolo Rossi and Ettore Vicari


We improve the theoretical estimates of the critical exponents for the threedimensional Heisenberg universality class. We find γ = 1.3960(9), ν = 0.7112(5), η = 0.0375(5), α = −0.1336(15), β = 0.3689(3), and δ = 4.783(3). We consider an improved lattice φ 4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the φ 4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios. PACS Numbers: 75.10.Hk, 75.10.–b, 05.70.Jk, 11.15.Me Typeset using REVTEX 1 TABLE I. Recent experimental estimates of the critical exponents for Heisenberg systems

Year: 2013
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