scholarly journals Critical behavior of the square lattice Blume–Capel model with an alternating anisotropy and next nearest neighbour interaction

2010 ◽  
Vol 3 (3) ◽  
pp. 1453-1457
Author(s):  
Shigenori Matsumoto ◽  
Nobuyasu Ito ◽  
Kazuo Hida
Keyword(s):  
Critical Behavior ◽  
Square Lattice ◽  
Nearest Neighbour ◽  
Neighbour Interaction

scholarly journals The zeros distribution of Z_5-symmetric model on a triangular lattice

2020 ◽  
Vol 16 (3) ◽  
pp. 307-313
Author(s):  
Siti Fatimah Zakaria ◽  
Nor Sakinah Mohd Manshur
Keyword(s):  
Partition Function ◽  
Complex Plane ◽  
Triangular Lattice ◽  
Square Lattice ◽  
Symmetric Model ◽  
Nearest Neighbour ◽  
Multiple Line ◽  
Lattice Graph ◽  
Zeros Of Partition Function ◽  
Neighbour Interaction

We study the -symmetric model with the nearest neighbour interaction between molecular dipole of five spin directions i.e. Q=5 which called as the -symmetric model on a triangular lattice. We investigate the zeros of partition function and the relationship to the phase transition. Initially, the model is defined on a triangular lattice graph with the nearest neighbour interaction. The partition function is then computed using a transfer matrix approach. We analyse the system by computing the zeros of the polynomial partition function using the Newton-Raphson method and then plot the zeros in a complex plane. For this lattice, the result shows that for specific type of energy level there are multiple line curves approaching real axis in the complex plane. The equation of the specific heat is produced and then plotted for comparison. Motivated from the work by Martin (1991) on models on square lattice, we extend the previous study to different lattice type that is triangular lattice.

scholarly journals The Z_6-symmetric model partition function on triangular lattice

2020 ◽  
Vol 16 (3) ◽  
pp. 264-270
Author(s):  
Nor Sakinah Mohd Manshur ◽  
Siti Fatimah Zakaria ◽  
Nasir Ganikhodjaev
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Triangular Lattice ◽  
Square Lattice ◽  
Partition Functions ◽  
Symmetric Model ◽  
Nearest Neighbour ◽  
Multiple Line ◽  
Multiple Phase ◽  
Neighbour Interaction

There is a study on a square lattice that can predict the existence of multiple phase transitions on a complex plane. We extend the study on the different types of ZQ-symmetric model and different lattices in order to provide more evidence to the existence of multiple phase transitions. We focus on the ZQ-symmetric model with the nearest neighbour interaction on the six spin directions between molecular dipole, i.e. Q = 6 on a triangular lattice. Mainly, the model is defined on the triangular lattice graph with the nearest neighbour interaction. By using the transfer matrix approach, the partition functions are computed for increasing lattice sizes. The roots of polynomial partition function are also computed and plotted in the complex Argand plane. The specific heat equation is used for further comparison. The result supports the existence of the multiple phase transitions by the emergence of the multiple line curves in the locus of zeros distribution for specific type of energy level.

The square lattice Ising model with frustrated nearest-neighbour interaction

1998 ◽  
Vol 254 (3-4) ◽  
pp. 267-272
Author(s):  
M. Badehdah ◽  
A. Benyoussef ◽  
M. Touzani
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Nearest Neighbour ◽  
Neighbour Interaction

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

scholarly journals Nearest-neighbour interaction from an Abelian symmetry and deviations from Hermiticity

2010 ◽  
Vol 690 (1) ◽  
pp. 62-67 ◽  
Author(s):  
G.C. Branco ◽  
D. Emmanuel-Costa ◽  
C. Simões
Keyword(s):  
Nearest Neighbour ◽  
Neighbour Interaction
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