1. Laws of thermodynamics 2. Thermodynamic relations 3. The ensemble theory 4. System Hamiltonians 5. The density matrix 6. The cluster variation method 7. Infinite series representations of correlation functions 8. The extended mean-field approximation 9. The exact Ising lattice identities 10. Propagation of short range order 11. Phase transition of the two-dimensional Ising model Appendix 1. The gamma function Appendix 2. The critical exponent in the tetrahedron approximation Appendix 3. Programming organization of the cluster variation method Appendix 4. A unitary transformation applied to the Hubbard Hamiltonian Appendix 5. Exact Ising identities on the diamond lattice References Subject index.1. Laws of thermodynamics 2. Thermodynamic relations 3. The ensemble theory 4. System Hamiltonians 5. The density matrix 6. The cluster variation method 7. Infinite series representations of correlation functions 8. The extended mean-field approximation 9. The exact Ising lattice identities 10. Propagation of short range order 11. Phase transition of the two-dimensional Ising model Appendix 1. The gamma function Appendix 2. The critical exponent in the tetrahedron approximation Appendix 3. Programming organization of the cluster variation method Appendix 4. A unitary transformation applied to the Hubbard Hamiltonian Appendix 5. Exact Ising identities on the diamond lattice References Subject index.

Cambridge University Press eBooksJan 1, 20020 citations

Numerical calculation of the thermodynamic properties of the Ising model on the square lattice

T. Morita

Physica A Statistical Mechanics and its ApplicationsJul 1, 19812 citations

Quasiclassical Methods in the Spin S, One Dimensional Ising Model

Robert L. Bowden, D. M. Kaplan, C. D. Graham +1 more

A Quasiclassical Spin Formalism is developed for spin algebras characteristic of Ising Models, that is, an algebra in which all elements commute. Spin operators and their products are mapped onto continous variables while traces are re‐expressed as integrals over these variables. Using the formalism, a certain Integral Equation is developed whose eigenfunctions and eigenvalues characterize the thermodynamical properties of the spin S, one dimensional Ising lattice. The kernel of the equation is the “classical” kernal in the limit as spin approaches infinity.A Quasiclassical Spin Formalism is developed for spin algebras characteristic of Ising Models, that is, an algebra in which all elements commute. Spin operators and their products are mapped onto continous variables while traces are re‐expressed as integrals over these variables. Using the formalism, a certain Integral Equation is developed whose eigenfunctions and eigenvalues characterize the thermodynamical properties of the spin S, one dimensional Ising lattice. The kernel of the equation is the “classical” kernal in the limit as spin approaches infinity.

AIP conference proceedingsJan 1, 19720 citations

Exploring Thermodynamic Features of the Three-Dimensional Ising Model

A. Chappars

APSOct 1, 20000 citations

Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model

Giovanni Feverati, Paul A. Pearce, Francesco Ravanini

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields $\\xi$ and $\\eta$ which play the role of the perturbing boundary fields $\\phi_{1,3}$ and $\\phi_{1,2}$ inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields $\\xi$ and $\\eta$ which play the role of the perturbing boundary fields $\\phi_{1,3}$ and $\\phi_{1,2}$ inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.

Feb 7, 20028 citations

\\xi

and

\\eta

which play the role of the perturbing boundary fields

\\phi_{1,3}

and

\\phi_{1,2}

inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.