Order parameter for non-mean-field spin glasses

Abstract

We propose a novel renormalization group (RG) method for non mean-field models of spin glasses, which leads to the emergence of a novel order parameter. Unlike previous approaches where the RG procedure is based on a priori notions on the system, our analysis follows a minimality principle, where no a priori assumption is made. We apply our approach to a spin-glass model built on a hierarchical lattice. In the RG decimation procedure, a novel order parameter spontaneously emerges from the system symmetries, and self-similarity features of the RG transformation only. This order parameter is the projection of the spin configurations on the ground state of the system. Kadanoff's majority rule for ferromagnetic systems is replaced by a more complex scheme, which involves such novel order parameter. The ground state thus acts as a pattern which translates spin configurations from one length scale to another. The rescaling RG procedure is based on a minimal, information-theory approach and, combined with the decimation, it yields a complete RG transformation. Below the upper critical dimension, the predictions for the critical exponent $\nu$, which describes the critical divergence of the correlation length, are in excellent agreement with numerical simulations from both this and previous studies. Overall, this study opens new avenues in the understanding of the critical ordering of realistic spin glasses, and it can be applied to spin-glass models on a cubic lattice and nearest-neighbor couplings which directly model spin-glass materials, such as AuFe, CuMn and other magnetic alloys.

References in corpus (24)

• Simulated Tempering: A New Monte Carlo Scheme
• Weak pairwise correlations imply strongly correlated network states in a neural population
• Thermodynamic signature of growing amorphous order in glass-forming liquids
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Ising spin glass transition in magnetic field out of mean-field
• Janus II: a new generation application-driven computer for spin-system simulations
• The correspondence between long-range and short-range spin glasses
• Ensemble renormalization group for disordered systems
• Generic replica symmetric field-theory for short range Ising spin glasses
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• Critical exponents and the correlation length in the charge exchange manganite spin glass Eu_{0.5}Ba_{0.5}MnO_{3}
• Real space Renormalization Group analysis of a non-mean field spin-glass
• Overlap Interfaces in Hierarchical Spin-Glass models
• Non-perturbative effects in spin glasses
• The ordered phase of the one-dimensional Ising spin glass with long-range interactions
• Renormalization Group Approach to Spin Glass Systems
• Finite-Dimensional Spin Glasses: States, Excitations, and Interfaces
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature