A scaling theory for the long-range to short-range crossover and an infrared duality*Dedicated to John Cardy on the occasion of his 70th birthday. (4th August 2017)

• Record Type: Journal Article
• Authors: Behan, Connor; Rastelli, Leonardo; Rychkov, Slava; Zan, Bernardo
• Is Part Of: Journal of physics. Volume 50:Number 35(2017)
• Publication Date: 2017-08-04
• Subjects: Ising model -- long-range interactions -- critical point -- conformal perturbation theory; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa8099
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study the second-order phase transition in the d -dimensional Ising model with long-range interactions decreasing as a power of the distance 1 / r d + s . For s below some known value s ∗, the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of s . At s = s ∗, the phase transition crosses over to the short-range universality class. While the location s ∗ of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality.