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TitleMathematical Physics, Analysis and Geometry - Volume 13
TagsPhysics
LanguageEnglish
File Size8.2 MB
Total Pages378
Table of Contents
                            Griffith−Kelly−Sherman Correlation Inequalities for Generalized Potts Model
	Abstract
On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window
	Abstract
		Introduction
		The Model
			The Hamiltonian
			Some Known Facts
			Preliminary: Cylindrical Coordinates
		The Result
		Numerical Computations
Inverse Problem for Sturm−Liouville Operators with Coulomb Potential which have Discontinuity Conditions Inside an Interval
	Abstract
Wegner Estimates for Some Random Operators with Anderson-type Surface Potentials
	Abstract
Perturbations of Functions of Operators in a Banach Space
	Abstract
Time-dependent Delta-interactions for 1D Schrödinger Hamiltonians
	Abstract
Pictorial Representation for Antisymmetric Eigenfunctions of PS−3 Integral Equations
	Abstract
From Uncertainty Principles to Wegner Estimates
	Abstract
		Introduction
		An Uncertainty Principle
		Spectral Averaging for General Measures
		Wegner Estimates
		References
The Escape Rate of a Molecule
	Abstract
Alternative Evaluation of a ln tan Integral Arising in Quantum Field Theory
	Abstract
Wegner-type Bounds for a Two-particle Lattice Model with a Generic fiRoughfl Quasi-periodic Potential
	Abstract
On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials
	Abstract
Comparison Theorems for Eigenvalues of Elliptic Operators and the Generalized Pólya Conjecture
	Abstract
Lagrangian Curves on Spectral Curves of Monopoles
	Abstract
		Lagrangian Curves on Holomorphic Curves
		A Different Characterization
		Lagrangian Curves on Spectral Curves
			The Charge 2 Monopole
			The Charge 3 Monopole
		Discussion
		References
On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations
	Abstract
The Representation of Isometric Operators on C1X
	The Representation of Isometric Operators on C1X
		Abstract
			Introduction
			Lemma
			Theorem
			References
Wegner Estimates for Sign-Changing Single Site Potentials
	Abstract
Numerical Range for Orbits Under a Central Force
	Abstract
		Introduction
		Angular Momentum and Central Force
		Orbits and Numerical Ranges
		An Example
		References
Mechanism of Energy Transfers to Smaller Scales Within the Rotational Internal Wave Field
	Abstract
D-bar Operators on Quantum Domains
	Abstract
                        
Document Text Contents
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Math Phys Anal Geom (2010) 13:1–18
DOI 10.1007/s11040-009-9063-1

Griffith–Kelly–Sherman Correlation Inequalities
for Generalized Potts Model

Nasir Ganikhodjaev · Fatimah Abdul Razak

Received: 22 April 2009 / Accepted: 8 July 2009 / Published online: 17 July 2009
© Springer Science + Business Media B.V. 2009

Abstract Inspired by the work of D.G.Kelly and S.Sherman on general
Griffiths inequalities on correlations in Ising ferromagnets, we formulate and
prove Griffith–Kelly–Sherman-type inequalities for the ferromagnetic Potts
model with a general number q of local states. We take as local state space for
the q-state Potts model the set Fc ={−l, −l+1, · · · , l−1, l},where l = q−1

2
. The

important properties of Fc for what follows are that |Fc| = q and Fc = −Fc.

Keywords Correlation inequalities · Potts model ·
Griffith–Kelly–Sherman inequalities · Gibbs measure

Mathematics Subject Classifications (2000) 82B20 · 82B26

1 Introduction

Statistical physics seeks to explain the macroscopic behavior of matter on the
basis of its microscopic structure. This includes the analysis of simplified math-
ematical models [3]. The Potts model [12] was introduced as a generalization of
the Ising model to more than two components (spins). Ising model considered

N. Ganikhodjaev (B) · F. A. Razak
Department of Computational and Theoretical Sciences,
Faculty of Science, IIUM, 25200 Kuantan, Malaysia
e-mail: [email protected]

F. A. Razak
e-mail: [email protected]

N. Ganikhodjaev
Institute of Mathematics and Information Technology,
100125, Tashkent, Uzbekistan

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http://arXiv.org/abs/math/0901.0123v1
http://arXiv.org/abs/math.QA/9808015
http://arXiv.org/abs/math.QA/9808037
http://arXiv.org/abs/math.QA/9808047
http://arXiv.org/abs/math.QA/9809002
http://arXiv.org/abs/math.QA/9809018
http://arXiv.org/abs/math/0711.3028
http://arXiv.org/abs/math/0912.0194

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