High-temperature expansion methods for Ising systems with quenched impurities

1979 ◽  
Vol 19 (9) ◽  
pp. 4631-4645 ◽  
Author(s):  
Ruth V. Ditzian ◽  
Leo P. Kadanoff
Keyword(s):  
High Temperature ◽  
Temperature Expansion ◽  
Ising Systems ◽  
High Temperature Expansion

High temperature multigraph expansions for general Ising systems

1981 ◽  
Vol 59 (1) ◽  
pp. 15-21 ◽  
Author(s):  
J. Oitmaa
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Square Lattice ◽  
Zero Field ◽  
Nearest Neighbour ◽  
Temperature Expansion ◽  
Graphical Information ◽  
Ising Systems ◽  
High Temperature Expansion ◽  
Multiple Edges

A high temperature expansion, in terms of connected graphs with single and multiple edges, is developed for general Ising systems with interactions of more than one type. The graphical information obtained is sufficient to derive 11 terms in the expansion of the high temperature zero-field susceptibility and 12 terms in the zero-field free energy for any Ising system. Series to this order are presented for the square lattice with nearest and next nearest neighbour interactions.

MONTE CARLO STUDY OF THE SPIN-1/2 HEISENBERG MODEL IN 1, 2, AND 3 DIMENSIONS

1991 ◽  
Vol 05 (13) ◽  
pp. 907-914 ◽  
Author(s):  
RICHARD J. CRESWICK ◽  
CYNTHIA J. SISSON
Keyword(s):  
Monte Carlo ◽  
High Temperature ◽  
Spin Wave ◽  
Heisenberg Model ◽  
Transition Probability ◽  
Lattice Models ◽  
Wave Theory ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Good Agreement

The properties of the spin-1/2 Heisenberg model on 1, 2, and 3-dimensional lattices are calculated using the Decoupled Cell Method of Homma et al., and these results are compared with high temperature and spin-wave expansions, and with other numerical approaches. The DCM has advantages over other Monte Carlo methods currently in wide use in that the transition probability is positive definite, there is no need to introduce an additional imaginary time, or Trotter, dimension, and the acceptance rate for transitions is comparable to that of classical lattice models. We find very good agreement between the DCM and the high temperature expansion in the temperature region where the high temperature expansion is valid, and reasonably good agreement at low temperatures with spin wave theory. The DCM fails for temperatures T < Tc which decreases with the size of the cell.

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