scholarly journals The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Zero-Field Partition Function and Correlation Length

2021 ◽  
Vol 10 (1) ◽  
pp. 38
Author(s):  
Jacques Curély
Keyword(s):  
Partition Function ◽  
Correlation Length ◽  
Square Lattice ◽  
Zero Field ◽  
Two Dimensional

Lattice statistics in a magnetic field. II. Order and correlations of a two-dimensional super-exchange antiferromagnet

1960 ◽  
Vol 256 (1287) ◽  
pp. 502-513 ◽  
Keyword(s):  
Magnetic Field ◽  
Long Range ◽  
Pair Correlation ◽  
Configurational Entropy ◽  
Square Lattice ◽  
Lattice Statistics ◽  
Zero Field ◽  
Two Dimensional ◽  
Ising Lattice ◽  
Pair Correlations

The long-range order and pair correlation functions of a two-dimensional super-exchange antiferromagnet in an arbitrary magnetic field are derived rigorously from properties of the standard square Ising lattice in zero field. (The model investigated was described in part I: it is a decorated square lattice with magnetic spins on the bonds coupled antiferromagnetically via non-magnetic spins on the vertices.) The behaviour near the transition temperature in a finite field is similar to that of the normal plane lattice, i. e. the long-range orders or spontaneous magnetizations of the sublattices vanish as ( T t – T ) ⅛ and the pair correlations behave as ω c + W ( T – T t ) ln | T – T t |. The configurational entropy is discussed and the anomalous entropy in the critical field at zero temperature is calculated exactly.

Lattice statistics in a magnetic field, I. A two-dimensional super-exchange antiferromagnet

1960 ◽  
Vol 254 (1276) ◽  
pp. 66-85 ◽  
Keyword(s):  
Magnetic Field ◽  
Critical Point ◽  
Continuous Functions ◽  
Square Lattice ◽  
Lattice Statistics ◽  
Zero Field ◽  
Two Dimensional ◽  
Small Fields ◽  
Arbitrary Magnetic Field ◽  
Ising Spins

The partition function of a two-dimensional ` super-exchange ’ antiferromagnet in an arbitrary magnetic field is derived rigorously. The model is a decorated square lattice in which magnetic Ising spins on the bonds are coupled together via non-magnetic Ising spins on the vertices. By use of the decoration transformation all the thermodynamic and magnetic properties of the model are derived from Onsager’s solution for the standard square lattice in zero field. The transition temperature T t (H) is a single-valued, decreasing function of the field H . The energy and the magnetization are continuous functions of T for all magnetic fields; but the specific heat and the temperature gradient of the magnetization become infinite as — In | T — T t |. The initial ( H = 0) susceptibility is a continuous and smoothly varying function of T with a maximum 40 % above the critical point; but ∂x/∂ T becomes infinite at T = T c . In a non-vanishing field the susceptibility has a logarithmic infinity at T = T t . For small fields the behaviour near the critical point is given by X ≈ ( N μ/ kT ) {2—√2— D ( T—T c ) ln ∣ T — T c ∣ — D´H 2 ln ∣ T — T c ∣}, where D and D' are constants.

HIGH-TEMPERATURE SUSCEPTIBILITY SERIES FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4919-4922
Author(s):  
KEH YING LIN ◽  
MALL CHEN
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Ising Model ◽  
Critical Exponent ◽  
Ising Models ◽  
Temperature Series ◽  
Square Lattice ◽  
Zero Field ◽  
Two Dimensional ◽  
Temperature Susceptibility

We have calculated the high-temperature series expansion of the zero-field susceptibility of the square-lattice Ising model with first and second neighbour interactions to the 20th order by computer. Our results extend the previous calculation by Hsiao and Lin to two more orders. We use the Padé approximants to estimate the critical exponent γ and the critical temperature. Our result 1.747 < γ < 1.753 supports the universality conjecture that all two-dimensional Ising models have the same critical exponent γ = 1.75.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

Two‐Dimensional V‐VI Binary Nanosheets with Square Lattice: A Theoretical Investigation

2021 ◽  
Author(s):  
Xin Qiao ◽  
Xiaodong Lv ◽  
Yinan Dong ◽  
Yanping Yang ◽  
Fengyu Li
Keyword(s):  
Theoretical Investigation ◽  
Square Lattice ◽  
Two Dimensional
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