NDLI: Magnetic properties of two-dimensional (2D) classical square Heisenberg lattices I- zero-field partition function

Content Provider	IEEE Xplore Digital Library
Author	Curély, J.
Copyright Year	2010
Description	Author affiliation: Centre de Physique Moléculaire Optique et Hertzienne (C.P.M.O.H.), Université Bordeaux 1 351 Cours de la Libération, 33405 Talence Cedex, France (Curély, J.)
Abstract	In this part labelled I we rigorously examine 2D square lattices composed of $(2N+1)^{2}$ classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg cou-plings). Each local operator exp(-α) $H^{ex}i,j)$ - where $H^{ex}i,j$ is the local exchange Hamiltonian associated with each site (i,j) - is expanded on the basis of spherical harmonics, each one being characterized by the couple of integers (ℓ,m), with ℓ≥0 and m∈[−ℓ,+ℓ]. Using spin lattice symmetries, we derive selection rules over these coefficients, thus allowing to express the zero-field partition function ZN(0). In the thermodynamic limit (N→∞), we show that the value m=0 is selected while ℓ=ℓ0≥0, ∀(i,j). A very simple closed-form expression may be then derived for ZN(0). Finally we report a thermal study of the current term of the characteristic polynomial giving ZN(0). We show that it appears crossovers between two consecutive terms characterized by integers ℓ and ℓ+1, respectively. Coming from high temperatures where the term characterized by ℓ=0 is dominant, near absolute zero, increasing ℓ-values are more and more selected when the temperature is cooling down. But, when T reaches zero, all the successive dominant terms become equivalent and are characterized by the value ℓ=0. We show that this property also prevails at T=0 K rigorously. This confirms the fact that, for a 2D lattice showing Heisenberg couplings, the critical temperature is TC=0 K, in agreement with Mermin-Wagner's theorem.
Starting Page	69
Ending Page	78
File Size	890499
Page Count	10
File Format	PDF
ISBN	9781424470198
ISSN	18420133
e-ISBN	9781424470204
DOI	10.1109/OPTIM.2010.5510415
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-05-20
Publisher Place	Romania
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Couplings Thermodynamics Temperature Electronic equipment Lattices Superconducting magnets Closed-form solution Statistics Magnetic semiconductors Magnetic properties
Content Type	Text
Resource Type	Article

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