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Register a new userInverse freezing in the Hopfield Fermionic Ising Spin Glass
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In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The Grand Canonical Potential is obtained within the static approximation and one-step replica symmetry breaking scheme. As a result, phase diagrams temperature {it versus} the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.
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We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field $Gamma$. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site $n$ is strongly affected by $Gamma$. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too.
It is well-known that spontaneous symmetry breaking in one spatial dimension is thermodynamically forbidden at finite energy density. Here we show that mirror-symmetric disorder in an interacting quantum system can invert this paradigm, yielding spontaneous breaking of mirror symmetry only at finite energy density and giving rise to mirror-glass order. The mirror-glass transition, which is driven by a finite density of interacting excitations, is enabled by many-body localization, and appears to occur simultaneously with the localization transition. This counterintuitive manifestation of localization-protected order can be viewed as a quantum analog of inverse freezing, a phenomenon that occurs, e.g., in certain models of classical spin glasses.
The stability of spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field $Gamma$. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues $lambda_{pm}$ of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when $Gamma$ is increased. Therefore, this result suggests that the study of the replicon can not be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the $lambda_{pm}$ indicate instability problems for the SG solution close to all range of first order boundary.
In conventional spin glasses, the magnetic interaction is not strongly anisotropic and the entire spin system freezes at low temperature. In La2(Cu,Li)O4, for which the in-plane exchange interaction dominates the interplane one, only a fraction of spins with antiferromagnetic correlations extending to neighboring planes become spin-glass. The remaining spins with only in-plane antiferromagnetic correlations remain spin-liquid at low temperature. Such a novel partial spin freezing out of a spin-liquid observed in this cold neutron scattering study is likely due to a delicate balance between disorder and quantum fluctuations in the quasi-two dimensional S=1/2 Heisenberg system.
All higher-spin s >= 1/2 Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s rightarrow infty. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of lambda = 1.93 and runaway exponent of y_R=0.24, showing simultaneous strong-chaos and strong-coupling behaviors. The ferromagnetic-spinglass-antiferromagnetic phase transitions occurring around p_t = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.
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