Randomly dilute spin models: a six-loop field-theoretic study

Abstract

We consider the Ginzburg-Landau MN-model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N -> 0 which describes the critical behaviour of an M-vector model in the presence of weak quenched disorder. We perform a detailed analysis of the perturbative series for the random Ising model (M=1). We obtain for the critical exponents: gamma = 1.330(17), nu = 0.678(10), eta = 0.030(3), alpha=-0.034(30), beta = 0.349(5), omega = 0.25(10). For M > 1 we show that the O(M) fixed point is stable, in agreement with general non-perturbative arguments, and that no random fixed point exists.

29 pages, RevTex

References in corpus (10)

• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• High precision Monte Carlo study of the 3D XY-universality class
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Five-loop renormalization-group expansions for the three-dimensional n-vector cubic model and critical exponents for impure Ising systems
• Random Fixed Point of Three-Dimensional Random-Bond Ising Models
• Stability of a cubic fixed point in three dimensions. Critical exponents for generic N
• Summability of the perturbative expansion for a zero-dimensional disordered spin model
• Observation of the Lambda Point in the 4He-Vycor System: A Test of Hyperuniversality
• High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

Cited by in corpus (72)

• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Coherent and dissipative dynamics at quantum phase transitions
• Large-n Critical Behavior of O(n)xO(m) Spin Models
• Universality class of 3D site-diluted and bond-diluted Ising systems
• Bond dilution in the 3D Ising model: a Monte Carlo study
• Smectic ordering in liquid crystal - aerosil dispersions II. Scaling analysis
• Disordered Systems and the Replica Method in AdS/CFT
• Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering
• The three-dimensional randomly dilute Ising model: Monte Carlo results
• Divergent Perturbation Series
• Critical properties of random anisotropy magnets
• Polymers in long-range-correlated disorder
• Randomly dilute Ising model: A nonperturbative approach
• The 3D +-J Ising model at the ferromagnetic transition line
• Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
• Short-time dynamics and critical behavior of three-dimensional site-diluted Ising model
• Weak quenched disorder and criticality: resummation of asymptotic(?) series
• Effective critical behaviour of diluted Heisenberg-like magnets
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Calculations of the dynamical critical exponent using the asymptotic series summation method
• Computer simulation of the critical behavior of 3D disordered Ising model
• Ising model on 3D random lattices: A Monte Carlo study
• Critical thermodynamics of three-dimensional chiral model for N > 3
• Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses
• Randomly dilute spin models with cubic symmetry
• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
• Critical behavior of magnetic systems with extended impurities in general dimensions
• Crossover behavior in three-dimensional dilute spin systems
• Relaxational dynamics in 3D randomly diluted Ising models
• Stability of critical behaviour of weakly disordered systems with respect to the replica symmetry breaking
• Large-n expansion for m-axial Lifshitz points
• Spin-density-wave order in cuprates
• Local and cluster critical dynamics of the 3d random-site Ising model
• Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder
• Universality classes of three-dimensional $mn$-vector model
• Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop εexpansion
• Disordered Ising model with correlated frustration
• Critical Behavior of the Three-Dimensional Ising model with Anisotropic Bond Randomness at the Ferromagnetic-Paramagnetic Transition Line
• Spin models with random anisotropy and reflection symmetry
• Surface critical behavior of random systems at the ordinary transition
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
• Wang-Landau study of the 3D Ising model with bond disorder
• Crossover effects in the bond-diluted Ising model in three dimensions
• Field-theory results for three-dimensional transitions with complex symmetries
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• On the Finite Size Scaling in Disordered Systems
• Surface critical behavior of random systems at the special transition
• Critical behavior of weakly disordered Ising model: Six-loop $\sqrt{\epsilon }$ expansion study
• Critical equation of state of randomly dilute Ising systems
• Six dimensional Landau-Ginzburg-Wilson theory
• Crossover from random-exchange to random-field critical behavior in Ising models
• Critical behavior of disordered systems with replica symmetry breaking
• Crossover between special and ordinary transitions in random semi-infinite Ising-like systems
• Three-dimensional Ising model confined in low-porosity aerogels: a Monte Carlo study
• Geometric and Nonequilibrium Criticality in Run-and-Tumble Particles with Competing Motility and Attraction
• Static and dynamic structure factors in three-dimensional randomly diluted Ising models
• Effect of weak disorder on the ground state of uniaxial dipolar spin systems in the upper critical dimension
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories
• Universal free-energy distribution in the critical point of a random Ising ferromagnet
• Effective and asymptotic criticality of structurally disordered magnets
• Two-loop Feynman integrals for ${\varphi }^4$ theory with long-range correlated disorder
• Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains
• Nonlinear susceptibilities of a weakly-disordered uniaxial ferromagnet in the critical region
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• Emergence of the 3D diluted Ising model universality class in a mixture of two magnets
• Surface critical behavior of semi-infinite systems with cubic anisotropy at the ordinary transition
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• High-order perturbative expansions of multi-parameter Phi^4 quantum field theories
• Critical exponents of the Ising model with quenched structural disorder and long-range interactions at spatial dimension $d=3$