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# High-temperature series for the RPn-1 lattice spin model (generalized Maier-Saupe model of nematic liquid crystals) in two space dimensions and with general spin dimensionality n.

Physical review. B, Condensed matter (Impact Factor: 3.66). 12/1992; 46(17):11141-11144. DOI: 10.1103/PhysRevB.46.11141

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**ABSTRACT:**We investigate a vectorial O(N) model with a generic nearest-neighbor interaction W(\bsigma_i\cdot \bsigma_j) (depending on {\cal N} tunable parameters), a Yukawa (and Gross Neveu) model with N_f fermions at finite temperature and the vectorial \phi^6 model, in the large N (N_f) limit. All this models exhibit a Mean Field critical point for N=\infinity. When 1/N fluctuations are included, infra red divergences appear near the critical point. In the framework of a generalized /N expansion we show that these divergences are related to a universal crossover mechanism between the Mean Field universality class (N=\infinity) and the nonclassical one for N04/2007; -
##### Article: Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

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**ABSTRACT:**We compute the phase diagram in the N→∞ limit for lattice RPN−1, CPN−1 and QPN−1σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.Nuclear Physics B 05/2001; 601(3):425–502. · 3.95 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We have considered a classical spin system, consisting of 3-component unit vectors, associated with a one-dimensional lattice {uk, k ∈ Z}, and interacting via translationally invariant pair potentials, isotropic in spin space, and of the long-range form where ∊ is a positive constant setting energy and temperature scales (i.e. T* = kBT/∊). Extending previous rigorous results, one can prove the existence of an ordering transition at finite temperature when 0 < σ < 1, and its absence when σ ≥ 1. We have studied the border case σ = 1, by means of computer simulation. Similarly to the magnetic counterparts of the present model, we found evidence suggesting a transition to a low-temperature phase with slow decay of correlations and infinite susceptibility, i.e. a Berezhinskiǐ–Kosterlitz–Thouless-like transition; the transition temperature was estimated to be Θ = 0.475 ± 0.005.International Journal of Modern Physics B 01/2012; 09(25). · 0.46 Impact Factor

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