Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation

Abstract

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF proportional to $L^{\theta }$, with $\theta$ the violation of hyperscaling critical exponent, and L the linear extension of the system. This modified behavior facilitates a number of new numerical approaches that can be used to locate critical points in random field systems from finite size simulation data. We test and confirm the new approaches on two random field systems in three dimensions, namely the random field Ising model, and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.

References in corpus (19)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Universality class of criticality in the restricted primitive model electrolyte
• Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?
• Precise determination of critical exponents and equation of state by field theory methods
• Lack of Self-Averaging in Critical Disordered Systems
• Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems
• Adsorption hysteresis and capillary condensation in disordered porous solids: a density functional study
• Monte Carlo study of the random-field Ising model
• Universality in Three Dimensional Random-Field Ground States
• Bond dilution in the 3D Ising model: a Monte Carlo study
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• New algorithm and results for the three-dimensional random field Ising Model
• Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2
• Critical behavior of colloid-polymer mixtures in random porous media
• First-order transition features of the 3D bimodal random-field Ising model
• Monte Carlo study of the Widom-Rowlinson fluid using cluster methods
• The Confined-Deconfined Interface Tension in Quenched QCD using the Histogram Method
• Colloid-polymer mixtures in random porous media: Finite size scaling and connected versus disconnected susceptibilities
• Critical behavior of the Widom-Rowlinson mixture: coexistence diameter and order parameter

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• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
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• Excitations in high-dimensional random-field Ising magnets
• Fluid-fluid demixing curves for colloid-polymer mixtures in a random colloidal matrix
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
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