Critical exponents of the spin-glass transition in a field at zero temperature

• 成果类型: Article
• 署名作者: Angelini, Maria Chiara; Palazzi, Saverio; Parisi, Giorgio; Rizzo, Tommaso
• 署名单位: Sapienza University Rome; Istituto Nazionale di Fisica Nucleare (INFN); Beihang University; Consiglio Nazionale delle Ricerche (CNR); Istituto di Nanotecnologia (NANOTEC-CNR); Consiglio Nazionale delle Ricerche (CNR); Istituto dei Sistemi Complessi (ISC-CNR)
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-8427
• DOI: 10.1073/pnas.2511882122
• 发表日期: 2025-09-16
• 关键词: renormalization-group approach; MODEL; symmetry

摘要

We analyze the spin-glass transition in a field in finite dimension D below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion is generated by the so-called M-layer construction, and it has 1/M as the associated small parameter. Computing analytically and numerically these nonstandard diagrams at first order in the 1/M expansion, we construct an e-expansion around the upper critical dimension D-uc= 8, with epsilon = D-uc-D. Following standard field theoretical methods, we can write a beta function, finding a new zero-temperature fixed-point associated with the spin-glass transition in a field in dimensions D < 8. We are also able to compute, at first order in the e-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent.