Dilute oriented loop models

Abstract

We study a model of dilute oriented loops on the square lattice, where each loop is compatible with a fixed, alternating orientation of the lattice edges. This implies that loop strands are not allowed to go straight at vertices, and results in an enhancement of the usual O(n) symmetry to U(n). The corresponding transfer matrix acts on a number of representations (standard modules) that grows exponentially with the system size. We derive their dimension and those of the centraliser by both combinatorial and algebraic techniques. A mapping onto a field theory permits us to identify the conformal field theory governing the critical range, $n\le 1$. We establish the phase diagram and the critical exponents of low-energy excitations. For generic n, there is a critical line in the universality class of the dilute O(2n) model, terminating in an SU(n+1) point. The case n=1 maps onto the critical line of the six-vertex model, along which exponents vary continuously.

32 pages, 13 figures. Version 2: minor changes

References in corpus (5)

• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Conformal boundary loop models
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• Combinatorial aspects of boundary loop models

Cited by in corpus (7)

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• On truncations of the Chalker-Coddington model
• Critical spin chains and loop models with $PSU(n)$ symmetry
• Special transitions in an O($n$) loop model with an Ising-like constraint