Theory Of Spin Glasses Research Articles

Toward a mean field theory for spin glasses

Abstract We find an approximate solution of the Sherrington-Kirkpatrick model for spin glasses; the internal energy and the specific heat are in very good agreement with the computer simulations, the zero temperature entropy is unfortunately negative, although it is very small.

The alternating magnetisation of 16.7 at.% CuMn

In some spin glasses, notably AuFe, the magnetisation and remanent moment below the spin glass temperature, Tf, are time-dependent of the magnetisation is observed in fields smaller than about 100 Oe, in contrast to present spin glass theories which predict slow relaxation below Tf. A possible explanation is that a threshold field exists below which relaxation is too rapid to observe on the usual laboratory time scales.

Fluctuation effects in spin glasses

This talk reviews recent work on the theory of spin glasses. The Edwards-Anderson approximation is explained and shown to be invalid even as a mean field theory because it predicts a certain positive definite correlation function to be negative. A method of restoring stability by breaking ’replica symmetry’ due to Bray and Moore is then discussed and shown to imply an infinite number of symmetry breakings in the ordered phase. Estimates of the ’lower critical dimension’ are reviewed. Several independent methods predict a value of four which, if correct, would imply that experiments have to be interpreted in terms of gradual freezing rather than a sharp phase transition. Finally we argue that the replica method gives correct results and previous difficulties arise from choosing an incorrect solution of the equations.

Validity and limitations of scaling laws in the theory of spin glasses

Current theories for the derivation of the internal-field distribution function for statistical models of spin-glasses are briefly reviewed, with reference to the form of the distribution function and the scaling behavior of the function itself and of related observable quantities. It is shown that deviations from scaling are inherent to the statistical theory itself and do not require separate mechanisms for their explanation, and the meaning of the currently-used Lorentzian-like forms of the distribution function is clarified.

On the mean field theory of spin glasses

The well known mean field equations for a spin glass described by an Ising model are solved analytically for temperatures close to the freezing temperature Tc. Specific heat, susceptibility and remanent magnetisation are obtained in terms of two parameters which have to be derived from a certain eigenvalue problem. Fluctuation effects are also discussed and it is shown that they are rather important.

On the fluctuation theory of spin glasses

We describe a spin glass by a random Ising model obeying the conditions Σ j J ij = 0. The mean field equations can be solved exactly near T c . Fluctuations decrease the susceptibility and increase the specific heat. Selfconsistent fluctuation equations are solved variationally above T c . According to this approximation specific heat and susceptibility are continuous at T c .

Random molecular fields in spin-glasses

The Edwards-Anderson theory of spin-glasses is derived without the replica method. It is conjectured that the mean-field free energy is less than the exact free energy.

Recent developments in the theory of spin glasses

The actual behavior of real spin glass systems bears little resemblance to that computed by the mean field like theories of Edwards, Anderson and Thouless, and Anderson and Palmer. There is no singularity in the specific heat, and there is an anomalous sensitivity to the magnetic field, for example. The reason has long been expected to be much bigger in this case than for conventional ferro- or antiferromagnetics. I will give a simple argument showing that the Heisenberg spin glass (such as Cu-Mn) is at ’’lower critical dimensionality’’, the lowest dimensionality at which fluctuations allow a phase transition to exist. As a result, its nearest relative is the 2-dimensional x-y model recently solved by Kosterlitz, and I will show how similar the real properties of spin glass are to those computed for the x-y model.

Evidence for a Ferromagnet—Spin-Glass Transition inPdFeMn

Measurements of the low-field ac susceptibility on ternary alloys of Pd + 0.35 at.% Fe and a Mn concentration of 0 to 8 at.% reveal, for three distinct regimes of Mn concentration, (a) a giant-moment ferromagnetism, (b) a high-temperature ferromagnetic phase followed by a lower-temperature spin-glass transition, and (c) a spin-glass phase. Our results for the susceptibility and the $T\ensuremath{-}c$ phase diagram are satisfactorily explained by the spin-glass theory of Sherrington and Kirkpatrick.

On the concept of local invariance in the theory of spin glasses

On the concept of local invariance in the theory of spin glasses

Generalised mean field theory of spin glasses

A generalised mean field theory of an Ising spin glass is presented which takes into account correlations between the spins and their interactions. The susceptibility chi (T) at zero temperature and the coefficient of the linear term in the specific heat for T to 0 tend to zero if spins and interactions are completely correlated (case I) and are largest (i.e. chi (0)=0.64 chi (Tf)) if they are uncorrelated (case II). With increasing correlations the slope of the cusp in the static susceptibility just below the freezing temperature Tf varies by a factor of 4. The temperature Tf is found to be proportional to the concentration c of magnetic impurities in case I and proportional to c1/2 in case II. The dependence of Tf on the mean free path l of the conduction electrons is investigated for the RKKY interaction as a special case. It turns out that Tf is much more sensitive to l in case I than in case II.

Phenomenological Theory of Spin-Glasses and Some Rigorous Results

A general phenomenological theory of spin-glasses is presented, which predicts the weak singularities (like cusps) of susceptibilities and specific heat near the transition point TsG and also predicts generally the divergence of the second derivative of the nonlinear suscepti­ bility with respect to a magnetic field in zero field at Tsa. A similar second derivative of specific heat is also shown to diverge at Tsa except for the molecular field theory. Scaling equations of state for magnetization m and spin-glass order-parameter q are derived, which yield new scaling relations of critical exponents for m(T), q(T), X,(T), Co(T) and the corresponding nonlinear quantities. These general results explain qualitatively very well the magnetic field dependence of magnetization and specific heat observed experimentally. A non-uniform phenomenological Hamiltonian is also proposed for the rcnormalization group approach, which yields the critical dimensionality d,=6, as usuaL Intermediate random statistics and real replica method are p;oposed. There is also presented an exactly soluble model showing a spin-glass like phase transition.

Comment on “The third law of thermodynamics and the theory of spin glasses” by E.P. Wohlfarth

Abstract A critical letter about the TAP theory of spin glasses is shown to be irrelevant, and some remarks about the “third law” of thermodynamics are made.

Comparison of the resistivity ofPdCr with canonical spin-glass systems

The electrical resistivity of several PdCr alloys, with between 11- and 18-at.% Cr, has been investigated between 1.4 and 300 K, and found to resemble that of canonical spin glasses (CSG). At low temperatures $\ensuremath{\Delta}\ensuremath{\rho}(T)\ensuremath{\propto}A{T}^{\frac{3}{2}}$, with $A\ensuremath{\propto}\ensuremath{-}logc$ over the concentration range investigated; the range of validity of this ${T}^{\frac{3}{2}}$ variation ($T<{T}_{1}$) is small in PdCr (where $A$ is comparatively large) as in AgMn. At higher temperatures $\ensuremath{\Delta}\ensuremath{\rho}(T)$ passes through an inflection point (at ${T}_{m}$) reaching a maximum (at ${T}_{\ensuremath{\mu}}$) above which it decreases with increasing temperature. The ratio $\frac{{T}_{m}}{{T}_{1}}$ is found to be roughly constant, as predicted by recent spin-glass theories, but as in CSG its magnitude is smaller than predicted. There are, however, several quantitative differences between PdCr and CSG; specifically both ${T}_{\ensuremath{\mu}}$ and $\ensuremath{\Delta}\ensuremath{\rho}({T}_{\ensuremath{\mu}})\ensuremath{-}\ensuremath{\Delta}\ensuremath{\rho}(0)$ are typically an order of magnitude smaller than in CSG of comparable concentration, whereas the slope of $\ensuremath{\Delta}\ensuremath{\rho}(T)$ above ${T}_{\ensuremath{\mu}}$ is about an order of magnitude larger than in CSG. This latter point in particular lends support to the assertion that such differences may arise from the fact that CSG are good moment systems (${T}_{K} or {T}_{S}\ensuremath{\ll}{T}_{m}$), but PdCr is not (${T}_{S}\ensuremath{\sim}{T}_{m}$).

A Note on the Theory of Spin Glasses

A Note on the Theory of Spin Glasses

The third law of thermodynamics and the theory of spin glasses

A theoretical description of spin glasses by Thouless, Anderson and Palmer is shown to violate the third law due to the use of an unjustified expression for the low temperature dependence of the Edwards-Anderson parameter.

Some comments on the theory of spin glasses

To explain the occurrence of the sharp cusp of the low-field susceptibility chi of spin glasses, some theories have been put forward which lead to a special type of phase transition at a critical temperature T0. It is shown that the straightforward application of such theories to deduce the magnetic part cm of the specific heat leads to some anomaly of this quantity at T0. More accurate measurements of cm and chi near T0 are necessary. At the moment it looks like a contradiction between theory and experiment.

Effective-field theory of the spin glass

An effective-field theory of the spin glass is presented, using only the conventional molecular-field approximation, in order to make the so-called replica formalism of the spin glass transparent.

Theory of spin glasses: Susceptibility and specific heat in a magnetic field

The magnetic field dependence of the susceptibility and specific heat of spin glasses is calculated in the frame of the Edwards-Anderson theory.

Static Properties of Spin Glasses

A recent classical theory for spin glasses of Edwards and Anderson is modified for the quantum mechanical case. One obtains a cusp in the susceptibility $\ensuremath{\chi}(T)$ and in the specific heat ${c}_{H}(T)$ at a characteristic temperature ${T}_{f}$ for finite spin $S$ and zero slope for $S\ensuremath{\rightarrow}\ensuremath{\infty}$. The specific heat is proportional to $T$ for $T\ensuremath{\rightarrow}0$, whereas it tends to the Boltzmann constant $k$ in the classical limit.