Critical exponents and equation of state of the three-dimensional Heisenberg universality class

Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Rossi, Paolo; Vicari, Ettore

doi:10.1103/physrevb.65.144520

Cited by 480 publications

(520 citation statements)

References 127 publications

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“…4(a) emphasizes the common crossing point at g c ∼ 2.52, which is indicative of a very weak T -dependence of 1/T 1 as the QCP is approached. Indeed, this behavior is consistent with early predictions 37 of universality in clean two-dimensional quantum antiferromagnets, according to which 1/T 1 ∼ T η , with η ≈ 0.0375, 38 and in the Kondo lattice model; 39 more on this in the Supplemental Material.…”

Section: Universal Behavior Of the Nmr Relaxation Ratesupporting

confidence: 88%

Impurities near an antiferromagnetic-singlet quantum critical point

et al. 2017

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Heavy fermion systems, and other strongly correlated electron materials, often exhibit a competition between antiferromagnetic (AF) and singlet ground states. Using exact Quantum Monte Carlo (QMC) simulations, we examine the effect of impurities in the vicinity of such AFsinglet quantum critical point (QCP), through an appropriately defined "impurity susceptibility," χimp. Our key finding is a connection, within a single calculational framework, between AF domains induced on the singlet side of the transition, and the behavior of the nuclear magnetic resonance (NMR) relaxation rate 1/T1. We show that local NMR measurements provide a diagnostic for the location of the QCP which agrees remarkably well with the vanishing of the AF order parameter and large values of χimp.

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Section: Universal Behavior Of the Nmr Relaxation Ratesupporting

confidence: 88%

Impurities near an antiferromagnetic-singlet quantum critical point

et al. 2017

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“…Performing this analysis we followed closely Refs. 30,18,17, where the models with 2, 3, and 4 components were studied. The determination of y 4,4 through Eq.…”

Section: Stability Of the O(5) Fixed Point A General Considerationsmentioning

confidence: 99%

Instability of O(5) multicritical behavior in SO(5) theory of high-Tcsuperconductors

Hasenbusch

Pelissetto²,

Vicari

2005

Phys. Rev. B

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We study the nature of the multicritical point in the three-dimensional O(3)⊕O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for the SO(5) theory of high-T c superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet.We investigate whether the O(3)⊕O( 2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent φ 4,4 = 0.180(15), in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop ǫ-expansion estimate φ 4,4 = 1/26, which has often been used in the literature to discuss the multicritical behavior within the SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition.We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems-high-T c cuprates should belong to this class-the multicritical point corresponds to a first-order transition.

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“…They should be compared with the values in table 2 which have been determined in this paper as follows: we take the values of ∆ φ for O(n) models with n = 2, 3, 4 calculated in refs. [34][35][36] as input and determine the scaling dimensions ∆ S , ∆ S , ∆ T and ∆ T using ∆ S -maximization. We repeat this procedure for the lower, central and upper value of ∆ φ given in these references and for different values of the cutoff ∆ * ∈ [18,23] and the number of points N ∈ [60, 120].…”

Section: A Closer Look At the Spectrum Of 3d O(n) Modelsmentioning

confidence: 99%

The effective bootstrap

Echeverri

Harling

Serone

2016

J. High Energ. Phys.

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Abstract:We study the numerical bounds obtained using a conformal-bootstrap method -advocated in ref.[1] but never implemented so far -where different points in the plane of conformal cross ratios z andz are sampled. In contrast to the most used method based on derivatives evaluated at the symmetric point z =z = 1/2, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test this "effective" bootstrap by studying the 3D Ising and O(n) vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature. We also determine the scaling dimensions of certain scalar operators in the O(n) vector models, with n = 2, 3, 4, which have not yet been computed using bootstrap techniques.

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Critical exponents and equation of state of the three-dimensional Heisenberg universality class

Cited by 480 publications

References 127 publications

Impurities near an antiferromagnetic-singlet quantum critical point

Impurities near an antiferromagnetic-singlet quantum critical point

Instability of O(5) multicritical behavior in SO(5) theory of high-Tcsuperconductors

The effective bootstrap

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