Kaviraj, Apratim Rychkov, Slava Trevisani, Emilio

We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric fixed point (Cardy, 1985), we look for interactions which may destabilize the SUSY RG flow and lead t...

Artigas, Danilo Bilski, Jakub Crowe, Sean Mielczarek, Jakub Trześniewski, Tomasz

The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is interesting to consider special and general relativistic extensions of such models. Here, we introduce a framewo...

Giuliani, Alessandro Mastropietro, Vieri Rychkov, Slava

Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non-perturbativ...

Boukraa, S. Maillard, J-M. Mccoy, B.M.

We present Painlev{\'e} VI sigma form equations for the general Ising low and high temperature two-point correlation functions $ C(M,N)$ with $M \leq N $ in the special case $\nu = -k$ where $\nu = \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$. More specifically four different non-linear ODEs depending explicitly on the two integers $M $ and $N$ emerge: thes...

Fortin, Jean-Yves

We consider itinerant spinless electrons moving as defects in a dilute two-dimensional Ising spin system, leading to an effective interaction mediated by spin fluctuations. Coupled self-consistent equations are analyzed after expressing the spin and fermion operators in terms of Grassmann variables. The effective mass, density of states, and specif...

Semkin, S. V. Smagin, V. P. Lyul’ko, V. I.
Published in
Physics of the Solid State

AbstractThe method of averaging over interaction fields has been analyzed as applied to the problems of statistical physics. This method has been theoretically justified as applied to a spin cluster. Based on the general relations obtained, approximate solutions for the bond-diluted Ising model are found. These approximate solutions are compared wi...

Rychkov, Slava

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders....

Belokon, V. I. Dyachenko, O. I. Lapenkov, R. V. Chibiriak, E. V.
Published in
Physics of Metals and Metallography

AbstractVarious types of magnetic ordering in two-sublattice magnetic materials with exchange interaction were studied using the method of random exchange interaction fields and the Ising model. The conditions for the magnetization of such systems were identified. Equations for the temperatures of phase transitions were derived.

Zinati, Alì Zanusso, O.

We discuss how a spin system, which is subject to quenched disorder, might exhibit multicritical behaviors at criticality if the distribution of the impurities is arbitrary. In order to provide realistic candidates for such multicritical behaviors, we discuss several generalizations of the standard randomly diluted Ising's universality class adopti...

Benedetti, Dario Gurau, Razvan Suzuki, Kenta
Published in
Journal of High Energy Physics

We continue the study of the bosonic O(N )3 model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant 𝜙4 composite operators, known as tetrahedron, pillow and double-trace. As shown in [1, 2], the tetrahedron operator is exactly marginal in the large-N limit and for a purely imaginary tetrahed...