| Modulation and correlations lengths in systems with competing interactions: new exponents and other universal features (2009) | |||||||||
Abstract | |||||||||
| We examine correlation functions in the presence of competing long and short interactions to find multiple correlation and modulation lengths. For many systems, we show the presence of a crossover temperature T^* above which there is no modulation and report on a new exponent, \nu_L, characterizing the universal nature of this divergence of the modulation length. We study large n systems and find, in general, that \nu_L = 1/2. We demonstrate that for a short range system frustrated by a general competing long range interaction, the crossover temperature T^* veers towards the critical temperature of the unfrustrated short range system (i.e., that in which the frustrating long range interaction is removed). We discover in systems with long range interactions the existence of at least one diverging correlation length in the high temperature limit. When screening is present, instead of diverging, this correlation length tends, at high temperatures to the screening length. We also show that apart from certain special crossover points, the total number of correlation and modulation lengths remains conserved. We derive an expression for the change in modulation length with temperature for a general system near the ground state with a ferromagnetic interaction and an opposing long range interaction. We illustrate that the correlation functions associated with the exact dipolar interactions, the correlation function differ substantially from those in which a scalar product form between the dipoles is assumed.. Comment: 16 pages, 8 figures | |||||||||
Details der Publikation | |||||||||
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