scholarly journals A Lorentzian inversion formula for defect CFT

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Pedro Liendo ◽  
Yannick Linke ◽  
Volker Schomerus
Keyword(s):  
Ising Model ◽  
Analytic Function ◽  
Crucial Role ◽  
Inversion Formula ◽  
Spin Variable ◽  
First Order ◽  
Large Spin

Abstract We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between bulk and defect expansions. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate one-point functions of the twist defect of the 3d Ising model to first order in the ϵ-expansion.

scholarly journals A generalized inversion formula for the continuous Jacobi transform

1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Analytic Function ◽  
Inversion Formula ◽  
Generalized Functions ◽  
Generalized Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Inversion ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

scholarly journals Wishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition

2020 ◽  
Vol 101 (5) ◽  
Author(s):  
Firas Hamze ◽  
Jack Raymond ◽  
Christopher A. Pattison ◽  
Katja Biswas ◽  
Helmut G. Katzgraber
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Order Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

1983 ◽  
Vol 61 (11) ◽  
pp. 1515-1527 ◽  
Author(s):  
James Glosli ◽  
Michael Plischke
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Ising Model ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbor ◽  
Universality Class ◽  
Energy Functional ◽  
First Order ◽  
Universality Classes

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

DYNAMICAL PHASE TRANSITION IN THE ISING MODEL ON A SCALE-FREE NETWORK

2005 ◽  
Vol 19 (32) ◽  
pp. 4769-4776 ◽  
Author(s):  
A. KRAWIECKI
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Ising Model ◽  
Tricritical Point ◽  
System Size ◽  
Critical Parameters ◽  
Dynamical Phase Transition ◽  
First Order ◽  
Dynamical Phase ◽  
Wide Range

Dynamical phase transition in the Ising model on a Barabási–Albert network under the influence of periodic magnetic field is studied using Monte-Carlo simulations. For a wide range of the system sizes N and the field frequencies, approximate phase borders between dynamically ordered and disordered phases are obtained on a plane h (field amplitude) versus T/Tc (temperature normalized to the static critical temperature without external field, Tc∝ ln N). On these borders, second- or first-order transitions occur, for parameter ranges separated by a tricritical point. For all frequencies of the magnetic field, position of the tricritical point is shifted toward higher values of T/Tc and lower values of h with increasing system size, i.e. the range of critical parameters corresponding to the first-order transition is broadened.

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