Variational Approach to Monte&nbsp;Carlo Renormalization Group

Wu, Yantao; Car, Roberto

doi:10.1103/physrevlett.119.220602

Variational Approach to Monte Carlo Renormalization Group

Journal Article · Tue Nov 28 00:00:00 EST 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.119.220602· OSTI ID:1541248

Wu, Yantao ^[1]; Car, Roberto ^[2]

Princeton Univ., NJ (United States). Dept. of Physics; DOE/OSTI
Princeton Univ., NJ (United States). Dept. of Chemistry

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. Here, the two-dimensional Ising model is used to illustrate the method.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-05ER46201; SC0017865

OSTI ID:: 1541248

Alternate ID(s):: OSTI ID: 1410481
OSTI ID: 1860491

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 22 Vol. 119; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (22)

Charge renormalization group in quantum field theory Bogoljubov, N. N.; šiekov, D. V. Il Nuovo Cimento, Vol. 3, Issue 5 https://doi.org/10.1007/BF02823486	journal	May 1956
A note on Green functions and the Ising model Callen, H. B. Physics Letters, Vol. 4, Issue 3 https://doi.org/10.1016/0031-9163(63)90344-5	journal	April 1963
The renormalization group and the ε expansion Wilson, K. Physics Reports, Vol. 12, Issue 2 https://doi.org/10.1016/0370-1573(74)90023-4	journal	August 1974
The Inverse Ising Problem Albert, Joseph; Swendsen, Robert H. Physics Procedia, Vol. 57 https://doi.org/10.1016/j.phpro.2014.08.140	journal	January 2014
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
Error estimates on averages of correlated data Flyvbjerg, H.; Petersen, H. G. The Journal of Chemical Physics, Vol. 91, Issue 1 https://doi.org/10.1063/1.457480	journal	July 1989
Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model Invernizzi, Michele; Valsson, Omar; Parrinello, Michele Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1618455114	journal	March 2017
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition Onsager, Lars Physical Review, Vol. 65, Issue 3-4 https://doi.org/10.1103/PhysRev.65.117	journal	February 1944
Quantum Electrodynamics at Small Distances Gell-Mann, M.; Low, F. E. Physical Review, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRev.95.1300	journal	September 1954
Monte Carlo calculation of renormalized coupling parameters. I. d = 2 Ising model Swendsen, Robert H. Physical Review B, Vol. 30, Issue 7 https://doi.org/10.1103/PhysRevB.30.3866	journal	October 1984
Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture Wilson, Kenneth G. Physical Review B, Vol. 4, Issue 9 https://doi.org/10.1103/PhysRevB.4.3174	journal	November 1971
Variational Approach to Enhanced Sampling and Free Energy Calculations Valsson, Omar; Parrinello, Michele Physical Review Letters, Vol. 113, Issue 9 https://doi.org/10.1103/PhysRevLett.113.090601	journal	August 2014
Renormalization-Group Approach to the Solution of General Ising Models Nauenberg, M.; Nienhuis, B. Physical Review Letters, Vol. 33, Issue 27 https://doi.org/10.1103/PhysRevLett.33.1598	journal	December 1974
Monte Carlo Renormalization Group Swendsen, Robert H. Physical Review Letters, Vol. 42, Issue 14 https://doi.org/10.1103/PhysRevLett.42.859	journal	April 1979
Dynamic Monte Carlo Renormalization Group Tobochnik, Jan; Sarker, Sanjoy; Cordery, Robert Physical Review Letters, Vol. 46, Issue 21 https://doi.org/10.1103/PhysRevLett.46.1417	journal	May 1981
Tricritical Universality in Two Dimensions Landau, D. P.; Swendsen, R. H. Physical Review Letters, Vol. 46, Issue 22 https://doi.org/10.1103/PhysRevLett.46.1437	journal	June 1981
Monte Carlo Calculation of Renormalized Coupling Parameters Swendsen, Robert H. Physical Review Letters, Vol. 52, Issue 14 https://doi.org/10.1103/PhysRevLett.52.1165	journal	April 1984
Nonuniversal critical dynamics in Monte Carlo simulations Swendsen, Robert H.; Wang, Jian-Sheng Physical Review Letters, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevLett.58.86	journal	January 1987
Scaling laws for ising models near T c Kadanoff, Leo P. Physics Physique Fizika, Vol. 2, Issue 6 https://doi.org/10.1103/PhysicsPhysiqueFizika.2.263	journal	June 1966
The renormalization group: Critical phenomena and the Kondo problem Wilson, Kenneth G. Reviews of Modern Physics, Vol. 47, Issue 4 https://doi.org/10.1103/RevModPhys.47.773	journal	October 1975
Quantum Electrodynamics at Small Distances Baker, M.; Johnson, K. Physical Review, Vol. 183, Issue 5 https://doi.org/10.1103/physrev.183.1292	journal	July 1969
Equation of state calculations by fast computing machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. https://doi.org/10.2172/4390578	report	March 1953

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Quantum momentum distribution and quantum entanglement in the deep tunneling regime Wu, Yantao; Car, Roberto The Journal of Chemical Physics, Vol. 152, Issue 2 https://doi.org/10.1063/1.5133053	journal	January 2020

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