Quantum critical point in the spin glass-antiferromagnetism competition for fermionic Ising Models

Abstract

The competition between spin glass ($SG$) and antiferromagnetic order ($AF$) is analyzed in two sublattice fermionic Ising models in the presence of a transverse $\Gamma$ and a parallel $H$ magnetic fields. The exchange interaction follows a Gaussian probability distribution with mean $-4J_0/N$ and standard deviation $J\sqrt{32/N}$, but only spins in different sublattices can interact. The problem is formulated in a path integral formalism, where the spin operators have been expressed as bilinear combinations of Grassmann fields. The results of two fermionic models are compared. In the first one, the diagonal $S^z$ operator has four states, where two eigenvalues vanish (4S model), which are suppressed by a restriction in the two states 2S model. The replica symmetry ansatz and the static approximation have been used to obtain the free energy. The results are showing in phase diagrams $T/J$ ($T$ is the temperature) {\it versus} $J_0/J$, $\Gamma /J$, and $H/J$. When $\Gamma$ is increased, $T_f$ (transition temperature to a nonergodic phase) reduces and the Neel temperature decreases towards a quantum critical point. The field $H$ always destroys $AF$; however, within a certain range, it favors the frustration. Therefore, the presence of both fields, $\Gamma$ and $H$, produces effects that are in competition. The critical temperatures are lower for the 4S model and it is less sensitive to the magnetic couplings than the 2S model.

15 pages, 6 figures, accepted in Physica A

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• Inverse freezing in the Hopfield Fermionic Ising Spin Glass
• A theoretical study of the cluster glass-Kondo-magnetic disordered alloys
• Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field
• One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin glass model in a transverse field
• Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field
• The spin glass-antiferromagnetism competition in Kondo-lattice systems in the presence of a transverse applied magnetic field