From localized to itinerant spin glasses: Grassmann field theory and mean-field solutions

Oppermann, R.H.; Müller–Groeling, Axel

doi:10.1016/0550-3213(93)90312-d

Cited by 30 publications

(61 citation statements)

References 9 publications

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“…A still different functional integral formulation consists in using Grassmann variables to write a field theory with an effective action where the spin operators in the Hamiltonian are expressed as bilinear combinations of fermions [9,10]. The advantage of the fermionic formulation is that it has a natural application to problems in condensed matter theory, where the fermion operators represent electrons that also participate in other physical processes, like superconductivity [11,12] and the Kondo effect [13].…”

Section: Introductionmentioning

confidence: 99%

The Ising spin glass in a transverse field revisited. Results of two fermionic models

Theumann¹,

Schmidt²,

Magalhães³

2002

Physica A: Statistical Mechanics and its Applications

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We analyze the long range Ising spin glass in a transverse field Γ by using Grassmann variables in a field theory where the spin operators are represented by bilinear combinations of fermionic fields. We compare the results of two fermionic models. In the four state (4S)-model the diagonal S z i operator has two vanishing eigenvalues, that are suppressed by a restraint in the two states (2S)-model. Within a replica symmetric theory and in the static approximation we obtain similar results for both models. They both exhibit a critical temperature T c (Γ) that decreases when Γ increases, until it reaches a quantum critical point (QCP) at the same value of Γ c and they are both unstable under replica symmetry breaking in the whole spin glass phase.

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Section: Introductionmentioning

confidence: 99%

The Ising spin glass in a transverse field revisited. Results of two fermionic models

Theumann¹,

Schmidt²,

Magalhães³

2002

Physica A: Statistical Mechanics and its Applications

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show abstract

“…Applying the same procedure to isotropic vector spin-glass model, we obtain the set of equations for diagonalq and non-diagonal q saddle point elements of Q matrix 43,44 :…”

Section: Semi-fermionic Representation For Spin Glass Modelsmentioning

confidence: 99%

“…The next step is to consider the second decoupling procedure for Tr[ Q X]. For this sake, following 43,44 we consider Q as a constant saddle-point matrix.…”

Section: Semi-fermionic Representation For Spin Glass Modelsmentioning

confidence: 99%

“…2 requires a replica-dependent decoupling field 44 . Although it is well known that both SK and isotropic vector model of infinite range spin glass are unstable with respect to Parisi's broken symmetry permutation symmetry 45 , we shall consider first the replica symmetrical solutions existing only near the phase transition point.…”

Section: Semi-fermionic Representation For Spin Glass Modelsmentioning

confidence: 99%

“…Following the procedure described in 43,44 we use fermionic representation of spin operators employing the replica trick 43 :…”

Section: Semi-fermionic Representation For Spin Glass Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Semi-Fermionic Representation for Spin Systems Under Equilibrium and Non-Equilibrium Conditions

Kiselev

2006

Int. J. Mod. Phys. B

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We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means of imaginary Lagrange multipliers resulting in special shape of quasiparticle distribution functions. We show how Schwinger-Keldysh technique for spin operators is constructed with the help of semi-fermions. We demonstrate how the idea of semi-fermionic representation might be extended to the groups possessing dynamic symmetries (e.g. singlet/triplet transitions in quantum dots). We illustrate the application of semi-fermionic representations for various problems of strongly correlated and mesoscopic physics.

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Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Oppermann

Binderberger

1994

Annalen der Physik

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We solve several low temperature problems of an infinite range metailic spin glass model. A compensation problem of T-0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of J-J,(T= 0). The critical value J,(T= 0) = 3/16pF1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter (Qab), a # b, the diagonal is confirmed as order parameter by the result

show abstract

From localized to itinerant spin glasses: Grassmann field theory and mean-field solutions

Cited by 30 publications

References 9 publications

The Ising spin glass in a transverse field revisited. Results of two fermionic models

The Ising spin glass in a transverse field revisited. Results of two fermionic models

Semi-Fermionic Representation for Spin Systems Under Equilibrium and Non-Equilibrium Conditions

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

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