Thermodynamic properties of the two-dimensional quantum Heisenberg ferromagnet and the effects of bond dilution

Journal Article · Tue Apr 01 04:00:00 EST 1986 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.33.4906· OSTI ID:6087424

Talbot, E F

The energy, the specific heat, and the magnetic susceptibility of the bond-diluted S = (1/2) Heisenberg ferromagnet on a two-dimensional square lattice are studied using a Monte Carlo sampling of the terms contributing to the partition function. The full lattice is studied in detail for sizes up to 20 x 20, and evidence is presented to suggest that the low-temperature correlation length behaves as xiapprox.e/sup nubetaJ/ with ..nu..approx.1.91 +- 0.06. The temperature dependence of the susceptibility, however, is not quite a simple exponential in ..beta..J. Knowledge of the correlation length and finite-size scaling allows the determination of the prefactor. Our conclusion is that the low-temperature susceptibility behaves as T/sup -1/e/sup 2nubetaJ/. Square lattices of size ranging from 6 x 6 to 12 x 12 are studied for k/sub B/T/J ranging from 0.1 to 3 and for several values of the bond probability p. Not surprisingly, the most drastic thermodynamic behavior near the critical bond-percolation probability is the sharp increase in the low-temperature susceptibility for p>p/sub c/. This corresponds to much larger correlation effects in the percolating lattice than below the percolation threshold. We also compare the thermodynamics at p = p/sub c/ to the scaling theories of Lubensky and Stanley et al. which suggest that the correlations at the percolation threshold are predominantly one dimensional.

• Research Organization: Department of Physics, University of California, Santa Barbara, California 93106
• OSTI ID: 6087424
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 33:7; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360104* -- Metals & Alloys-- Physical Properties
BINDING ENERGY
CRYSTAL MODELS
DILUTION
ENERGY
FERROMAGNETIC MATERIALS
HEISENBERG MODEL
LOW TEMPERATURE
MAGNETIC MATERIALS
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
MATERIALS
MATHEMATICAL MODELS
MONTE CARLO METHOD
PHYSICAL PROPERTIES
SPECIFIC HEAT
TEMPERATURE DEPENDENCE
THERMODYNAMIC PROPERTIES
TWO-DIMENSIONAL CALCULATIONS