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Fermionic van Hemmen Spin Glass Model with a Transverse Field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $Γ$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by $Γ$. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential $μ$ and $Γ$. The $Γ$ field suppresses the magnetic orders. The increase of $μ$ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by $μ$. In addition, $μ$ can change the nature of the phase boundaries introducing a first order transition.