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Determination of the critical manifold tangent space and curvature with Monte Carlo renormalization group

Journal Article · · Physical Review E
 [1];  [2]
  1. Princeton Univ., NJ (United States); DOE/OSTI
  2. Princeton Univ., NJ (United States)
+ Show Author Affiliations
We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. Furthermore, we study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0017865
OSTI ID:
1612762
Alternate ID(s):
OSTI ID: 1860499
OSTI ID: 1558836
Journal Information:
Physical Review E, Journal Name: Physical Review E Journal Issue: 2 Vol. 100; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (23)

Conformal Field Theory book January 1997
Tests for Monte Carlo renormalization studies on Ising models journal February 1986
Riemannian structure on manifolds of quantum states journal September 1980
Curvature formulas for implicit curves and surfaces journal October 2005
Scaling and Renormalization in Statistical Physics book January 2015
92 Years of the Ising Model: A High Resolution Monte Carlo Study journal April 2018
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition journal February 1944
Monte Carlo renormalization-group study of the rectangular Ising ferromagnet: Universality and a fixed line journal September 1984
Monte Carlo renormalization-group study of tricritical behavior in two dimensions journal June 1986
Critical behavior of the spin- 3 2 Blume-Capel model in two dimensions journal May 1998
Thermodynamic geometry, phase transitions, and the Widom line journal November 2012
Geometric critical exponents in classical and quantum phase transitions journal October 2014
Information geometry and the renormalization group journal November 2015
Variational Approach to Enhanced Sampling and Free Energy Calculations journal August 2014
Variational Approach to Monte Carlo Renormalization Group journal November 2017
Renormalization-Group Approach to the Solution of General Ising Models journal December 1974
Monte Carlo Renormalization Group journal April 1979
Quantum Critical Scaling of the Geometric Tensors journal August 2007
Information-Theoretic Differential Geometry of Quantum Phase Transitions journal September 2007
Two-Dimensional Ising Model as a Soluble Problem of Many Fermions journal July 1964
Static Phenomena Near Critical Points: Theory and Experiment journal April 1967
The renormalization group: Critical phenomena and the Kondo problem journal October 1975
Riemannian geometry in thermodynamic fluctuation theory journal July 1995

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Monte Carlo Methods
Monte Carlo methods
Physics
Renormalization
Statistical Physics