We show that tricritical points displaying unusual behavior exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one-loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ tricritical point of metallic quantum spin glasses are derived.
We show that tricritical points displaying unusual behavior exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one-loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new T=0 tricritical point of metallic quantum spin glasses are derived.
We present details of the phase diagrams of fermionic systems with random and frustrated interactions, emphasizing the important role of the chemical potential. The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations, being controlled by quantum statistics. We compare the spin density diluted Sherrington-Kirkpatrick spin glass with classical spin 1 models such as the BEG model. We analyse in detail the infinite range model and show that spin glass order must decay discontinuously as the chemical potential exceeds a critical value, provided the temperature is below the tricritical one, and that the T=0 transition is of classical type. Parisi replica permutation symmetry breaking (RPSB) governs the thermal spin glass transitions and fermionic modifications of the SK-models AT-line emerge. RPSB takes place everywhere within the fermionic spin glass phase. Although the critical field theory of the quantum paramagnet to spin glass transition in metallic systems remains replica--symmetric at T=0, with only small corrections at low T from RPSB, the phase diagram is affected at O(T^0) by RPSB. Generalizing our results for the fermionic Ising spin glass we consider aspects of models with additional spin and charge quantum--dynamics such as metallic spin glasses.
The present work analyzes the fermionic Ising spin glass model in a transverse magnetic field. The problem is written in the Grand Canonical ensemble with the spin operators represented by bilinear combinations of fermionic fields. The transverse field is a spin "flip" mechanism and inserts quantum fluctuations, which can lead the transition temperature Tj to quantum critical point (QCP). In this case, the phase transition from spin glass to paramagnetic phases occurs in T = o. On the other hand, charge fluctuations controlled by chemical potentiall-L show the existence of a tricritical point. The replica method with replica symmetry and static approximation are used to solve this problem. However, the replica symmetry solution shows some problems, like negative entropy in low temperatures. Thus, the stability conditions are derived to test the generated solution of this IDodel. The main purpose of this work is to study the competition between spin glass and paramagnetic phases with both quantum and charge fluctuations. After the stability conditions are derived, a detailed sight into the generated solution is shown under the form of diagrams phase. The stability conditions, however, show another applications in the present problem, once they can be used, for instance, in the tricritical point derivation.
Engineering long-range interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian mean-field model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the many-body system through a first-order quantum phase transition from an ordered to a disordered phase. At higher temperatures, the fluctuation-induced phase transition remains first order initially and switches to second-order only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with long-range couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and mean-field theory.
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field Γ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of Γ and for system sizes N≤16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of Γ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γc≃1.5. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get z=2.1±0.1 which is in contradiction with a recent estimate (z=4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ<Γc.
In this work we use field-theoretic and renormalization-group methods to study the finite-temperature ferromagnetic phase transition in the three-dimensional Hubbard model. We show that the nature of the ferromagnetic transition may strongly depend on the constraint imposed on the system. For example, if the system is allowed to exchange particles with a reservoir, the stability criterion for the occurrence of a continuous phase transition can be calculated using the mean-field approximation. On the other hand, if the total charge is conserved and charge- and spin-density fluctuations are considered in the theory, a different criterion, quite distinct from the mean-field one, is found, resulting in a fluctuation-induced renormalized Heisenberg tricritical point. The tricritical behavior is studied by calculating the one-loop renormalized free energy and using scaling analysis to determine the tricritical exponents. Finally, the exact solution of the model in the spherical limit and near the ferromagnetic transition is presented, in which case no fluctuation-induced tricritical point is found.
We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.