Sine-square deformation applied to classical Ising models

Abstract

Sine-square deformation (SSD) is a treatment proposed in quantum systems, which spatially modifies a Hamiltonian, gradually decreasing the local energy scale from the center of the system toward the edges by a sine-squared envelope function. It is known to serve as a good boundary condition as well as to provide physical quantities reproducing those of the infinite-size systems. We apply the SSD to one- and two-dimensional classical Ising models. Based on the analytical calculations and Monte Carlo simulations, we find that the classical SSD system is regarded as an extended canonical ensemble of a local subsystem each characterized by its own effective temperature. This effective temperature is defined by normalizing the system temperature by the deformed local energy scale. A single calculation for a fixed system temperature provides a set of physical quantities of various temperatures that quantitatively reproduce well those of the uniform system.

arXiv comment15pages 8 figures

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Cited by in corpus (4)

• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Sine-square deformed mean-field theory
• Scan calculation of the density of states: real space cluster perturbation theory applied to inhomogeneous Hubbard model in one dimension
• Exact Quench Dynamics from Thermal Pure Quantum States