A Test of Scaling Theory on the Critical Isotherm

1972 ◽  
Vol 50 (24) ◽  
pp. 3117-3122 ◽  
Author(s):  
D. D. Betts ◽  
L. Filipow
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Excellent Agreement ◽  
Critical Behavior ◽  
Critical Exponents ◽  
High Field ◽  
Two Dimensional ◽  
Amplitude Ratios ◽  
Critical Amplitude ◽  
Critical Isotherm

Using recently extended data of Sykes et al. on the high field expansion of the free energy of the two-dimensional spin-1/2 Ising model the critical behavior of the magnetization and its first six temperature derivatives are examined on the critical isotherm. The estimates of the critical exponents and the critical amplitude ratios are found to be in reasonable to excellent agreement with scaling theories.

Calculating the conformal charge from the second moment of the spin–spin correlation function

1993 ◽  
Vol 442 (1915) ◽  
pp. 485-488 ◽  
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
High Field ◽  
Central Charge ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Extrapolation Methods ◽  
Amplitude Ratios ◽  
Spin Correlation Function ◽  
Second Moment

We develop high field expansions for the second moment of the spin–spin correlation function of the two-dimensional Ising model at arbitrary temperature T . Setting T = T c and approaching the critical point along the field direction, this quantity has a 1/ h 2 , divergence as the external field h goes to zero. The amplitude for this divergence is estimated by series extrapolation methods, and is shown to lead to an estimate for the central charge of 0.50 by using Cardy’s formula for the central charge in terms of hyperuniversal amplitude ratios.

ISING MODEL IN THE MAGNETIC FIELD iπkT/2

1988 ◽  
Vol 02 (03n04) ◽  
pp. 471-481 ◽  
Author(s):  
K. Y. LIN ◽  
F. Y. WU
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Ising Model ◽  
Zero Field ◽  
Two Dimensional ◽  
Anisotropic Interactions ◽  
The Magnetic Field ◽  
Explicit Expressions

It is shown that the free energy and the magnetization of an Ising model in the magnetic field H = iπkT/2 can be obtained directly from corresponding expressions of these quantities in zero field, provided that the latter are known for sufficiently anisotropic interactions. Using this approach we derive explicit expressions of the free energy and the magnetization at H = iπkT/2 for a number of two-dimensional lattices.

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

JETP Letters ◽  
2018 ◽  
Vol 107 (9) ◽  
pp. 569-576 ◽  
Author(s):  
V. V. Prudnikov ◽  
P. V. Prudnikov ◽  
E. A. Pospelov ◽  
P. N. Malyarenko
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Two Dimensional

scholarly journals CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

2001 ◽  
Vol 12 (02) ◽  
pp. 257-271
Author(s):  
X.-N. LI ◽  
J. MACHTA
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Cluster Algorithm ◽  
The Other ◽  
Square Lattice ◽  
Critical Dynamics ◽  
Two Dimensional ◽  
Cluster Algorithms ◽  
Dynamic Exponent

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

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