Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Renormalization group and fractal cluster model of spin glasses

M. A. Contínentino, S. Moss de Oliveira

Published Apr 1, 1988• 3 citations
Publisher

Abstract

Recent dynamic experiments on spin glasses, in which contours of constant relaxation time are obtained in the plane of magnetic field versus temperature, are discussed from a renormalization-group point of view. We show that two fixed points control the critical behavior of spin glasses and the critical exponents associated with them can be determined through the dynamic experiments. We give a renormalization-group formulation of the fractal cluster model of spin glasses.

DOI
10.1103/physrevb.37.5877

Related papers

Dynamic scaling and the field-dependent critical line in a fractal cluster model of spin glasses

M. A. Contínentino, A. P. Malozemoff

We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line ${T}_{g}$(H). Above the zero-field transition temperature ${T}_{g}$, M(t) follows a stretched exponential form exp(-${t}^{1\mathrm{\ensuremath{-}}n}$) with n=\ensuremath{\nu}z/(\ensuremath{\varphi}+\ensuremath{\nu}z), where \ensuremath{\varphi},\ensuremath{\nu}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region ${T}_{g}$(H)${T}_{g}$ in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.

Physical review. B, Condensed matter•Mar 1, 1986•44 citations

Relaxation behavior of fractal-cluster spin glasses

L. Lundgren, Per Nordblad, Peter Svedlindh

The relaxation behavior of spin glasses has been analyzed in the framework of the critical fractal-cluster model. It is found that the relaxation rate of the magnetization can be expressed as $\frac{\ensuremath{\partial}m}{\ensuremath{\partial}\mathrm{ln}t}\ensuremath{\propto}{t}^{\ensuremath{-}\frac{\ensuremath{\beta}}{z\ensuremath{\nu}}}\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\tau}}_{\ensuremath{\xi}}})}^{\frac{\ensuremath{\beta}\ensuremath{\delta}}{z\ensuremath{\nu}}}]$, where $\ensuremath{\beta}$, $\ensuremath{\delta}$, $z$, $\ensuremath{\nu}$ are standard static and dynamic critical exponents and ${\ensuremath{\tau}}_{\ensuremath{\xi}}$ is the relaxation time of a characteristic cluster which diverges at the spin-glass freezing temperature ${T}_{g}$. The expression is valid through ${T}_{g}$ and is found to describe excellently the fundamental features of the relaxation in real spin glasses.

Physical review. B, Condensed matter•Dec 1, 1986•31 citations

Spin Glass in a Field: A New Zero-Temperature Fixed Point in Finite Dimensions

Maria Chiara Angelini, Giulio Biroli

By using real-space renormalization group (RG) methods, we show that spin glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-standing debate about the behavior of spin glasses in a field.

arXiv:1409.1011•Physical Review Letters•Mar 4, 2015•49 citations

Physical model for static and dynamic scaling in spin glasses

A. P. Malozemoff, B. Barbara

We extend earlier critical fractal cluster models of a spin glass phase transition. At the transition temperature in finite field, a negative excluded-volume term dominates a positive saturated-cluster term, giving the negative H2/δ nonlinear susceptibility observed experimentally. The two competing effects in general have different relaxation times and therefore novel implications for dynamic scaling.

Journal of Applied Physics•Apr 15, 1985•48 citations

Ising Spin Glasses : interaction distribution dependence of the critical exponents

Pierre‐Olivier Mari, Ian A. Campbell

Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been carried out on Ising Spin Glasses in dimension three, using a technique where corrections to finite size scaling can be controled. The data show that the critical exponents vary strongly as a function of the kurtosis of the interaction distribution, a parameter which from the standard point of view should not be pertinent. This observation implies that for spin glasses the renormalization group analysis should not be approached in a the same way as in the case of canonical second order transitions; a much richer structure of universality classes would appear to exist for spin glasses.

arXiv:cond-mat/0111174•Nov 9, 2001•5 citations

Critical Properties of Spin-Glasses

A. Brooks Harris, T. C. Lubensky, Jing-Huei Chen

The critical properties of the model of a spin-glass proposed by Edwards and Anderson are studied using the renormalization group. The critical exponents are calculated in $6\ensuremath{-}\ensuremath{\epsilon}$ spatial dimensions. It is argued that a tricritical point can exist where the nonordering field is the skewness of the distribution of $J$.

Physical Review Letters•Feb 23, 1976•234 citations
Recent dynamic experiments on spin glasses, in which contours of constant relaxation time are obtained in the plane of magnetic field versus temperature, are discussed from a renormalization-group point of view. We show that two fixed points control the critical behavior of spin glasses and the critical exponents associated with them can be determined through the dynamic experiments. We give a renormalization-group formulation of the fractal cluster model of spin glasses.
We extend an earlier fractal cluster model of spin glasses to study (1) the magnetization relaxation M(t) induced by a magnetic field, (2) magnetic noise, and (3) dynamics near a critical line Tg{T}_{g}Tg​(H). Above the zero-field transition temperature Tg{T}_{g}Tg​, M(t) follows a stretched exponential form exp(-${t}^{1\mathrm{\ensuremath{-}}n}$) with n=\ensuremath{\nu}z/(\ensuremath{\varphi}+\ensuremath{\nu}z), where \ensuremath{\varphi},\ensuremath{\nu}, and z are standard static and dynamical critical exponents. A dynamic scaling relation is derived for the entire region Tg{T}_{g}Tg​(H)Tg{T}_{g}Tg​ in agreement with experiments. The equations associated with lines of constant relaxation time are obtained and it is shown how nonuniversality of exponents along the critical line can be tested.
The relaxation behavior of spin glasses has been analyzed in the framework of the critical fractal-cluster model. It is found that the relaxation rate of the magnetization can be expressed as $\frac{\ensuremath{\partial}m}{\ensuremath{\partial}\mathrm{ln}t}\ensuremath{\propto}{t}^{\ensuremath{-}\frac{\ensuremath{\beta}}{z\ensuremath{\nu}}}\mathrm{exp}[\ensuremath{-}{(\frac{t}{{\ensuremath{\tau}}_{\ensuremath{\xi}}})}^{\frac{\ensuremath{\beta}\ensuremath{\delta}}{z\ensuremath{\nu}}}]$, where $\ensuremath{\beta}$, $\ensuremath{\delta}$, zzz, $\ensuremath{\nu}$ are standard static and dynamic critical exponents and ${\ensuremath{\tau}}_{\ensuremath{\xi}}$ is the relaxation time of a characteristic cluster which diverges at the spin-glass freezing temperature Tg{T}_{g}Tg​. The expression is valid through Tg{T}_{g}Tg​ and is found to describe excellently the fundamental features of the relaxation in real spin glasses.
By using real-space renormalization group (RG) methods, we show that spin glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-standing debate about the behavior of spin glasses in a field.
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been carried out on Ising Spin Glasses in dimension three, using a technique where corrections to finite size scaling can be controled. The data show that the critical exponents vary strongly as a function of the kurtosis of the interaction distribution, a parameter which from the standard point of view should not be pertinent. This observation implies that for spin glasses the renormalization group analysis should not be approached in a the same way as in the case of canonical second order transitions; a much richer structure of universality classes would appear to exist for spin glasses.
The critical properties of the model of a spin-glass proposed by Edwards and Anderson are studied using the renormalization group. The critical exponents are calculated in $6\ensuremath{-}\ensuremath{\epsilon}$ spatial dimensions. It is argued that a tricritical point can exist where the nonordering field is the skewness of the distribution of JJJ.