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Monday, August 3, 2020 | History

2 edition of Series expansions for lattice models found in the catalog.

Series expansions for lattice models

by Cyril Domb

  • 290 Want to read
  • 37 Currently reading

Published by Academic Press in London .
Written in English

    Subjects:
  • Fase-overgangen,
  • Kritische verschijnselen

  • Edition Notes

    Statementedited by C. Domb and M.S. Green
    SeriesPhase transitions and critical phenomena -- v. 3.
    Classifications
    LC ClassificationsQC175.16.P5 D65 v.3
    The Physical Object
    Paginationxviii, 694 p.
    Number of Pages694
    ID Numbers
    Open LibraryOL27080573M
    ISBN 100122203038
    ISBN 109780122203039
    OCLC/WorldCa35529534

    The accomplishments and the available expertise of scientists working on spin systems, lattice gauge models, and quantum liquids and solids has culminated in an extraordinary opportunity for rapid and efficient development of realistic strategies and algorithms of ab initio theoretical analysis of. We calculate the area, edge and corner Renyi entanglement entropies in the ground state of the transverse-field Ising model, on a simple-cubic lattice, by high-field and low-field series expansions. We find that while the area term is positive and the line term is negative as required by strong subadditivity, the corner contributions are positive in 3-dimensions. Analysis of the series.

    Generalized Series Expansions in Asymptotically Free Large-N Lattice Field Theories Pavel Buividovich (Regensburg University) Resurgence in Gauge and String Theories, Lissabon, July I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e., what dynamical systems people would call Lindstedt r, from what I heard, this series (for QFT case) is known to have zero radius of convergence, and it causes tons of difficulties in theory.

      Many of the studies using finite lattice method series expansions have considered various cases of the q-state Potts model. The initial application of the finite lattice method by de Neef () was an expansion for the q = 3 case in powers : I G Enting. The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics.. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and.


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Series expansions for lattice models by Cyril Domb Download PDF EPUB FB2

Early chapters cover the classical treatment of critical phenomena through high-temperature expansions, and introduce graph theoretical and combinatorial algorithms. The book then discusses high-order linked-cluster perturbation expansions for quantum lattice models, Cited by: This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated electron systems and elementary by: Abstract.

Chapter 1 begins by discussing the origin of the partition method for a power series expansion. Then the reader is introduced to the method as it is applied to the basic transcendental functions of cosecant, secant and the reciprocal of the logarithmic function, ln ⁡ (1 + z).The coefficients of the resulting power series expansions obtained from the two trigonometric functions are.

Preface; 1. Introduction; 2. High- and low-temperature expansions for the Ising Model; 3. Models with continuous symmetry and the free graph expansion; 4. Quantum spin models at T = 0; 5. Quantum antiferromagnets at T = 0; 6. Correlators, dynamical structure factors and multi-particle excitations; 7.

Quantum spin models at finite temperature; 8. Electronic models; 9. Review of lattice gauge Cited by: Get this from a library. Series expansion methods for strongly interacting lattice models. [Jaan Oitmaa; Christopher Hamer; Weihong Zheng] -- "This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated.

Add tags for "Phase transitions and critical phenomena / Vol. 3, Series expansions for Series expansions for lattice models book models.". Be the first. This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly.

Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in. Derivation of the Main Result. The main idea behind this paper is that the low temperature series expansion of the partition function, Z(x), of any lattice model can be easily obtained from the low temperature series expansion of the corresponding free energy, f(x).In this article we consider the Ising model on a square lattice in the so-called bulk by: 2.

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square by: 2. Part of the Theoretical and Mathematical Physics book series (TMP) Abstract In this chapter we discuss methods for obtaining coefficients in the expansions of partition functions and free energies, or their derivatives, in a series of powers of temperature-dependent variables.

UCLEAR PHYSIC~ PROCEEDINGS SUPPLEMENTS ELSb:Vlk:R Nuclear Physics B (Proc. Suppl.) 47 () Series Expansions from the Finite Lattice Method I.G. Enting~ CSIRO, Division of Atmospheric Research, Private Bag 1, Mordialloc, VicAustralia The finite lattice method has proved a powerful technique for obtaining exact series expansions for problems in lattice by:   The corner transfer matrix formalism is used to obtain low-temperature series expansions for the square lattice Ising model in a field.

This algebraic technique appears to be far more efficient than conventional methods based on combinatorial by: For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models.

Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice : Springer Netherlands.

The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef―Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts : David A.

Lavis. SERIES EXPANSION METHODS FOR STRONGLY INTERACTING LATTICE MODELS Series Expansion Methods for Strongly Interacting Lattice Models Jaan Oitmaa, Chris Hamer and Weihong Zheng Series Expansion Methods for Strongly Interacting Lattice Models Jaan Oitmaa, Chris Hamer and Weihong Zheng.

Ising, heisenberg and hubbard models in relation to insulating and metallic ferro- and antiferro-magnets.- Studies of lattice spin systems using series expansions.- Application of linked-cluster expansions to quantum hamiltonian lattice systems.- Critical properties of Price: $ : Phase Transitions and Critical Phenomena.

Vol. 3; Series Expansions for Lattice Models () and a great selection of similar New, Used and Collectible Books available now at Format: Hardcover. ular, the usefulness of mean-field approaches (hydrodynamic equations, cluster expansions) is demonstrated time and again throughout the book’s many examples.

“Nonequilibrium Phase Transitions in Lattice Models” is sure to become a standard reference guide for the field, and it will hopefully motivate much of the future research.

ing of repetitive lattice structures has been steadily increasing. Therefore, there is a need to broaden awareness among practicing engineers and research workers of the recent developments in various aspects of continuum modeling for large lattice structures.

The present paper is a File Size: 3MB. Pages in category "Lattice models" The following 55 pages are in this category, out of 55 total. This list may not reflect recent changes (). This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series.

These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular.Our group studies quantum lattice models, which may represent atomic spins in a magnet, electrons in a superconductor, or quarks confined within the proton.

Various methods of treating such models have been employed including series expansions, Monte Carlo simulations, exact diagonalization and the density matrix renormalization group (DMRG).