Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

Sergio Caracciolo; Bortolo Matteo Mognetti; Andrea Pelissetto

doi:10.1016/j.nuclphysb.2004.11.027

paper

Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

arXiv:cond-mat/0409536 · doi:10.1016/j.nuclphysb.2004.11.027

Abstract

We investigate a two-dimensional classical $- v ec t or m o d e l w i t ha g e n er i c n e a r es t - n e i g hb or in t er a c t i o n$ W(\bsigma_i\cdot \bsigma_j) $in t h e l a r g e - N l imi t, f oc u s in g o n t h e f ini t e - t e m p er a t u r e t r an s i t i o n p o in t a tw hi c h e n er g y - e n er g y cor r e l a t i o n s b eco m ecr i t i c a l . W es h o w t ha tt hi s t r an s i t i o nb e l o n g s t o t h e I s in g u ni v er s a l i t y c l a ss . H o w e v er, t h e w i d t h o f t h er e g i o nin w hi c h I s in g b e ha v i or i so b ser v e d sc a l es a s$ 1/N^{3/2} $a l o n g t h e ma g n e t i c d i r ec t i o nan d a s 1/ N in t h e t h er ma l d i r ec t i o n; o u t s i d e a cr osso v er t o m e an - f i e l d b e ha v i or occ u r s . T hi se x pl ain s w h y o n l y m e an - f i e l d b e ha v i or i so b ser v e df or$ N=\infty$

34 pages, 1 figure

Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections

Abstract

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