De Polsi Gonzalo, Balog Ivan, Tissier Matthieu, Wschebor Nicolás
Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay.
Institute of Physics, Bijenička cesta 46, HR-10001 Zagreb, Croatia.
Phys Rev E. 2020 Apr;101(4-1):042113. doi: 10.1103/PhysRevE.101.042113.
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.
通过实施非微扰重整化群的导数展开至次下领头阶（通常记为(O(∂^{4}))），我们计算了(O(N))模型在不同(N)值下的临界指数(ν)、(η)和(ω)。我们分析了该近似方案在连续阶次下的行为，并观察到其与一个小参数（通常在(1/9)到(1/4)之间）的明显收敛，这与伊辛模型的先前研究结果相符。这使我们能够给出有充分依据的误差范围。我们得到的临界指数测定精度与大多数场论技术所获得的精度相近或更好。在某些物理相关情形下，我们的精度也优于蒙特卡罗模拟。在(O(2))情形中，对于比热指数(α)，蒙特卡罗估计值与实验值之间存在长期争议，我们的结果与蒙特卡罗结果相符，但明显排除了实验值。
