Scaling behavior of the ising model coupled to two-dimensional quantum gravity

1992 ◽  
Vol 45 (8) ◽  
pp. 2957-2962 ◽  
Author(s):  
S. M. Catterall ◽  
J. B. Kogut ◽  
R. L. Renken
Keyword(s):  
Ising Model ◽  
Quantum Gravity ◽  
Scaling Behavior ◽  
Two Dimensional

ISING MODEL SIMULATIONS ON THE MANIFOLDS OF TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (17) ◽  
pp. 1615-1628 ◽  
Author(s):  
M. E. AGISHTEIN ◽  
C. F. BAILLIE
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Quantum Gravity ◽  
Cluster Algorithm ◽  
Sampling Technique ◽  
Analytical Prediction ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Model Simulations ◽  
Second Order Phase Transition

The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.

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