Monte Carlo renormalization-group study of the three-dimensional Ising model

Journal Article · Fri May 01 04:00:00 EDT 1992 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.45.10438· OSTI ID:7113611

Baillie, C F ^[1]; Gupta, R ^[2]; Hawick, K A; Pawley, G S ^[3]

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1. Physics Department, University of Colorado, Boulder, Colorado 80309 (United States)
2. T-8, MS-B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Physics Department, Edinburgh University, Edinburgh EH9 3JZ (United Kingdom)

We present results of a Monte Carlo renormalization-group study of the three-dimensional Ising model on 64{sup 3} and 128{sup 3} simple-cubic lattices. The eigenvalues of a linearized transformation matrix, constructed with the use of 53 even operators and 46 odd operators, are shown to be free of truncation errors. Our estimate of the critical coupling is 0.221 652{plus minus}0.000 003{plus minus}0.000 001 where the first error is statistical and the second due to the finite number of blocking steps. The results for the relevant exponents are {nu}=0.624(2) and {eta}=0.026(3). This estimate for {nu} lies (2--3){sigma} below that obtained from other methods. The correction-to-scaling exponent is found to lie in the range {omega}=0.8--0.85. We also find that the subleading magnetic exponent is relevant and present evidence that it corresponds to a redundant eigenvector of the majority-rule blocking transformation.

• DOE Contract Number: FG03-85ER25009
• OSTI ID: 7113611
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 45:18; ISSN PRBMD; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPUTERIZED SIMULATION
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
CUBIC LATTICES
ERRORS
ISING MODEL
MATHEMATICAL MODELS
MONTE CARLO METHOD
SIMULATION
THREE-DIMENSIONAL CALCULATIONS