De Polsi G, Balog I, Tissier M, Wschebor N. Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group.
Phys Rev E 2020;
101:042113. [PMID:
32422800 DOI:
10.1103/physreve.101.042113]
[Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 02/26/2020] [Indexed: 06/11/2023]
Abstract
We compute the critical exponents ν, η and ω of O(N) models for various values of N by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted O(∂^{4})]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter, typically between 1/9 and 1/4, compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field-theoretical techniques. We also reach a better precision than Monte Carlo simulations in some physically relevant situations. In the O(2) case, where there is a long-standing controversy between Monte Carlo estimates and experiments for the specific heat exponent α, our results are compatible with those of Monte Carlo but clearly exclude experimental values.
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