Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
| Autor: | Gonzalo De Polsi, Matthieu Tissier, Nicolás Wschebor, Ivan Balog |
|---|---|
| Přispěvatelé: | Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
O(N) model critical behavior functional renormalization group Monte Carlo method FOS: Physical sciences expansion: derivative 01 natural sciences 010305 fluids & plasmas O(2) Error bar 0103 physical sciences Statistical physics universality renormalization group: nonperturbative 010306 general physics Condensed Matter - Statistical Mechanics Physics Specific heat Statistical Mechanics (cond-mat.stat-mech) [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Statistical Physics higher-order: 2 Renormalization group O(N) [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] Universality (dynamical systems) High Energy Physics - Theory (hep-th) Exponent Ising model specific heat numerical calculations: Monte Carlo Critical exponent |
| Zdroj: | Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2020, 101 (4), pp.042113. ⟨10.1103/PhysRevE.101.042113⟩ |
| ISSN: | 1539-3755 1550-2376 |
| DOI: | 10.1103/PhysRevE.101.042113⟩ |
| Popis: | We compute the critical exponents $\nu$, $\eta$ and $\omega$ 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 $\mathcal{O}(\partial^4)$]. 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 longstanding controversy between Monte-Carlo estimates and experiments for the specific heat exponent $\alpha$, our results are compatible with those of Monte-Carlo but clearly exclude experimental values. |
| Databáze: | OpenAIRE |
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