We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O(N)-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from 2−1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.
Exact results for the O(N) model with quenched disorder / Delfino, Gesualdo; Lamsen, Noel. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2018:4(2018), pp. 1-10. [10.1007/JHEP04(2018)077]
Exact results for the O(N) model with quenched disorder
Delfino, Gesualdo;Lamsen, Noel
2018-01-01
Abstract
We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for O(N)-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder parameters: a modulus that vanishes when approaching the pure case, and a phase angle. The critical lines fall into three classes depending on the values of the disorder modulus. Besides the class corresponding to the pure case, a second class has maximal value of the disorder modulus and includes Nishimori-like multicritical points as well as zero temperature fixed points. The third class contains critical lines that interpolate, as N varies, between the first two classes. For positive N , it contains a single line of infrared fixed points spanning the values of N from 2−1 to 1. The symmetry sector of the energy density operator is superuniversal (i.e. N -independent) along this line. For N = 2 a line of fixed points exists only in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless phase observed in presence of disorder.File | Dimensione | Formato | |
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