Finite Lattice Calculations on Discrete Models

2006 ◽  
Vol 3 (2) ◽  
pp. 296-300
Author(s):  
M. J. Velgakis
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Finite Lattice ◽  
Nearest Neighbors ◽  
Discrete Models ◽  
New Method ◽  
Stat Phys ◽  
Power Demand ◽  
Lattice Calculations ◽  
Computer Power

A new method is proposed for the calculation of the exact partition function for Ising-like systems, based on finite-lattice arguments. In a way, the method is originated with the finite scaling theories presented by Bhanot [J. Stat. Phys. 60, 55 (1990)] and earlier by Binder [Physica 62, 508 (1972)]. The method is tested on a 2D Ising model with nearest- and next-nearest-neighbors interactions. An asset of the method is the low computer power demand.

A new method for the partition function of discrete systems with application to the 3D Ising model

1987 ◽  
Vol 183 (3-4) ◽  
pp. 331-336 ◽  
Author(s):  
Gyan Bhanot ◽  
Steve Black ◽  
Paul Carter ◽  
Román Salvador
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Discrete Systems ◽  
New Method ◽  
3D Ising Model

Finite-lattice calculations for the two-dimensional axial-next-nearest-neighbor Ising model

1981 ◽  
Vol 24 (11) ◽  
pp. 6632-6641 ◽  
Author(s):  
G. O. Williams ◽  
P. Ruján ◽  
H. L. Frisch
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Finite Lattice ◽  
Two Dimensional ◽  
Lattice Calculations

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

scholarly journals Automatic contraction of unstructured tensor networks

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Adam Jermyn
Keyword(s):  
Partition Function ◽  
Statistical Physics ◽  
Discrete Models ◽  
Correlation Structure ◽  
Central Problem ◽  
Partition Functions ◽  
Lattice Systems ◽  
Tensor Networks ◽  
Tensor Network

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

scholarly journals Some new results on Yang-Lee zeros of the Ising model partition function

1996 ◽  
Vol 215 (5-6) ◽  
pp. 271-279 ◽  
Author(s):  
Victor Matveev ◽  
Robert Shrock
Keyword(s):  
Ising Model ◽  
Partition Function
Sign in / Sign up

Export Citation Format

Share Document