An exact functional relation for the partition function of a 2D Ising model with magnetic field

1988 ◽  
Vol 21 (11) ◽  
pp. L599-L601 ◽  
Author(s):  
H J Giacomini
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Partition Function ◽  
Functional Relation

EXACT RESULTS FOR THE ISING MODEL ON A 3–12 LATTICE

1989 ◽  
Vol 03 (08) ◽  
pp. 1237-1245
Author(s):  
K.Y. LIN
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Ising Model ◽  
Partition Function ◽  
Functional Relation ◽  
Interaction Parameters ◽  
Zero Field ◽  
Exact Results ◽  
Kagome Lattice ◽  
Kagomé Lattice

We consider the Ising model on a 3–12 lattice with magnetic field. An exact functional relation is established for the partition function and our result is a generalization of Giacomini’s work on the Kagomé lattice. We calculate the zero-field magnetic susceptibility when an appropriate relation among the interaction parameters is satisfied.

scholarly journals EXACT PARTITION FUNCTION AND BOUNDARY STATE OF CRITICAL ISING MODEL WITH BOUNDARY MAGNETIC FIELD

1995 ◽  
Vol 10 (12) ◽  
pp. 973-984 ◽  
Author(s):  
R. CHATTERJEE
Keyword(s):  
Magnetic Field ◽  
Renormalization Group ◽  
Ising Model ◽  
Partition Function ◽  
Ground State ◽  
Renormalization Group Flow ◽  
Conformal Boundary ◽  
Boundary State ◽  
Ground State Degeneracy ◽  
Group Flow

We compute the exact partition function of the 2-D Ising Model at critical temperature but with nonzero magnetic field at the boundary. The model describes a renormalization group flow between the free and fixed conformal boundary conditions in the space of boundary interactions. For this flow the universal ground state degeneracy g and the full boundary state is computed exactly.

scholarly journals Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity

1997 ◽  
Vol 12 (22) ◽  
pp. 1605-1627 ◽  
Author(s):  
J. Ambjørn ◽  
K. N. Anagnostopoulos ◽  
U. Magnea
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Partition Function ◽  
Quantum Gravity ◽  
Complex Plane ◽  
Dynamical Triangulations ◽  
Complex Temperature ◽  
Complex Magnetic Field ◽  
Real Temperature ◽  
Ising Spins

We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte–Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.

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