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Register a new userCritical exponents in spin glasses : numerics and experiments
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Added by
Lorenzo W. Bernardi
Publication date
1999
fields
Physics
and research's language is
English
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We give an overview of numerical and experimental estimates of critical exponents in Spin Glasses. We find that the evidence for a breakdown of universality of exponents in these systems is very strong.
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For a mean-field classical spin system exhibiting a second-order phase transition in the stationary state, we obtain within the corresponding phase space evolution according to the Vlasov equation the values of the critical exponents describing power-law behavior of response to a small external field. The exponent values so obtained significantly differ from the ones obtained on the basis of an analysis of the static phase-space distribution, with no reference to dynamics. This work serves as an illustration that cautions against relying on a static approach, with no reference to the dynamical evolution, to extract critical exponent values for mean-field systems.
Results are given for the ground state energy and excitation spectrum of a simple $N$-state $Z_N$ spin chain described by free parafermions. The model is non-Hermitian for $N ge 3$ with a real ground state energy and a complex excitation spectrum. Although having a simpler Hamiltonian than the superintegrable chiral Potts model, the model is seen to share some properties with it, e.g., the specific heat exponent $alpha=1-2/N$ and the anisotropic correlation length exponents $ u_parallel =1$ and $ u_perp=2/N$.
The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation length -- appear. We indeed observe power laws and scaling behavior over extraordinarily many decades of the suitable scaling variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe films. However, we find that, when the putative critical point is approached, the singular behavior of thermodynamic quantities transforms into an analytic one: the critical point does not exist, it is replaced by a more complex phase involving domains of opposite magnetization, below as well as $above$ the putative critical temperature. All essential experimental results are reproduced by Monte-Carlo simulations in which, alongside the familiar exchange coupling, the competing dipole-dipole interaction is taken into account. Our results imply that a scaling behavior of macroscopic thermodynamic quantities is not necessarily a signature for an underlying second-order phase transition and that the paramagnetic-to-ferromagnetic phase transition proceeds, very likely, in the presence of at least two long spatial scales: the correlation length and the size of magnetic domains.
Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormalization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the phi^4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the lambda-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.
Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., $beta, gamma, u$) vary keeping others (e.g., $delta , eta$) fixed. Here we report a ferromagnetic phase transition in (Sm$_{1-y}$Nd$_{y}$)$_{0.52}$Sr$_{0.48}$MnO$_3$ $(0.5le yle1)$ single crystal where all critical exponents vary with $y.$ Such variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multicriticality.
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