Commensurate and Incommensurate O(n) Spin Systems: Novel Even-Odd Effects, A Generalized Mermin-Wagner-Coleman Theorem, and Ground States

Details Commensurate and Incommensurate O(n) Spin Systems: Novel Even-Odd Effects, A Generalized Mermin-Wagner-Coleman Theorem, and Ground States Commensurate and Incommensurate O(n) Spin Systems: Novel Even-Odd Effects, A Generalized Mermin-Wagner-Coleman Theorem, and Ground States

2001-05-14

arxiv.org/abs/cond-mat/0105253v12

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We examine n component spin systems with arbitrary two spin interactions (of unspecified range) within a general framework to highlight some new subtleties present in incommensurate systems. We determine the ground states of all translationally invariant O(n>1) systems and prove that barring commensurability effects they are always spiral- no other ground states are possible. We study the effect of thermal fluctuations on the ground states to discover a novel odd-even n effect. Soft spin analysis suggests that algebraic long range order is possible in certain frustrated incommensurate even n systems while their odd n counterparts exhibit an exponential decay of correlations. We illustrate that many frustrated incommensurate continuous spin systems display smectic like thermodynamics. We report on a generalized Mermin-Wagner-Coleman theorem for all two dimensional systems (of arbitrary range) with analytic kernels in momentum space. A new relation between generalization Mermin-Wagner-Coleman bounds and dynamics is further reported. We suggest a link between a generalized Mermin-Wagner-Coleman theorem to divergent decoherence (or bandwidth) time scale in the quantum context. A generalization of the Peierls bound for commensurate systems with long range interactions is also discussed. We conclude with a discussion of O(n) spin dynamics in the general case.

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