Low-temperature solution of the Sherrington-Kirkpatrick model

I propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x --> 0, Bx --> infinity of the Parisi replica symmetry breaking scheme parameter . The distribution function of the frozen fields has been known to develop a linear gap at zero temperature. The scaling equations are integrated to find an exact numerical value for the slope of the gap thetaP(x,y)/delta|(y --> 0) = 0.301 046.... I also use the scaling solution to devise an inexpensive numerical procedure for computing finite time scale (x =1) quantities. The entropy, the zero field cooled susceptibility, and the local field distribution function are computed in the low-temperature limit with high precision, barely achievable by currently available methods.     

Chaos in temperature in the Sherrington-Kirkpatrick model

We prove the existence of chaos in temperature in the Sherrington-Kirkpatrick model. The effect is exceedingly small, namely, of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behavior of the overlap distribution function PT1(,T2)(q) in finite-size systems.     

Double Dirac cones at k = 0 in pinned platonic crystals

In this paper, we compute the band structure for a pinned elastic plate which is constrained at the points of a hexagonal lattice. Existing work on platonic crystals has been restricted to square and rectangular array geometries, and an examination of other Bravais lattice geometries for platonic crystals has yet to be made. Such hexagonal arrays have been shown to support Dirac cone dispersion at the center of the Brillouin zone for phononic crystals, and we demonstrate the existence of double Dirac cones for the first time in platonic crystals here. In the vicinity of these Dirac points, there are several complex dispersion phenomena, including a multiple interference phenomenon between families of waves which correspond to free space transport and those which interact with the pins. An examination of the reflectance and transmittance for large finite gratings arranged in a hexagonal fashion is also made, where these effects can be visualized using plane waves. This is achieved via a recurrence relation approach for the reflection and transmission matrices, which is computationally stable compared to transfer matrix approaches.     

Magnetic phase diagram of perovskite Mn oxides at T = 0

Minimizing total free energy by numerical calculations, we obtain the magnetic phase diagram of perovskite Mn oxides, such as with , Ca, Sr, etc. in the whole doping region from x =0 to x =1 at temperature T =0. It is discovered that a spiral state is stable in a low concentration of X ions while a canted state is stable in a high concentration of X ions, and a ferromagnetic phase can exist in the intermediate concentrations when the antiferromagnetic interaction is weak. The energy difference between spiral and canted states is found to be small when the Hund coupling is large. Magnetic field induced spiral/canted phase transition is considered as a possible mechanism of the colossal magnetoresistance (CMR) in the Mn oxides. Received: 11 July 1996 / Revised: 7 December 1996 / Accepted: 24 July 1997     

Single-particle model for the frequency dependence of weak infrared absorption in crystals and molecules at T = 0 K

We obtain a simple expression for the infrared absorption coefficient α within the single-particle model at zero temperature. For potentials admitting harmonic approximation, α is found to decrease nearly exponentially with increasing frequency for small anharmonicity, with departures for larger anharmonicity. Potentials which do not admit harmonic approximation display a frequency dependence of the power-law variety. The present results in the quantum limit are similar to those obtained in the classical limit by Mills and Maradudin.     

On the Superfluid Fraction of an Arbitrary Many-Body System at T=0

I derive a set of sufficient and (barring certain pathologies) necessary conditions for a one-component system with velocity-independent forces to have a super-fluid fraction ρ _s /ρ equal to unity at zero temperature: In addition to a condition closely related (but not obviously equivalent) to the usual one of off-diagonal long-range order, the ground state should possess unbroken invariance under both spatial translation and time reversal. Some generalizations are made to the case of multicomponent systems.     

Random Ising model in the magnetic field at T = 0: I. The distribution of the effective fields

The integral equation for the distribution function of the effective fields in the random Ising model in the finite external field is solved exactly at zero temperature in the one-dimensional case for 1) dilute ferromagnet, 2) dilute antiferromagnet and 3) ±J model. The ground state characteristics of these systems are obtained. In particular the effective fields in the ±J model are shown to have a triangular distribution in the zero external field limit.     

Entanglement scaling in the one-dimensional Hubbard model at criticality

We derive exact expressions for the local entanglement entropy epsilon in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field h or chemical potential mu. The leading divergences of delta epsilon/delta h and delta epsilon/delta mu are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.     

Small amplitude forced fluid dynamics from gravity at T=0

The usual derivative expansion of gravity duals of charged fluid dynamics is known to break down in the zero temperature limit. In this case, fluid–gravity duality is not understood precisely. We explore this problem for a zero temperature charged fluid driven by a low frequency, small amplitude and spatially homogeneous external force. In the gravity dual, this corresponds to a time dependent boundary value of the dilaton. We calculate the bulk solution for the dilaton and the leading back reaction to the metric and the gauge fields using the modified low frequency expansion of Faulkner et al. (arXiv:0907.2694 [hep-th]). The resulting solutions are regular everywhere, establishing fluid–gravity duality to this order.     

Metastability range of the Bose condensate in 7Li-fermion mixtures at T = 0

We evaluate the ground state of a mixture of bosons and spin-polarized fermions in the case of attractive boson-boson interactions, using a variational Ansatz for the Bose condensate wave function and the Thomas-Fermi approximation for the fermions in the mean field of the condensate. Within this approximation we show that the presence of the fermions tends to restrict the metastability range of the condensate, irrespectively of the sign of the boson-fermion interactions. Numerical illustrations are reported for mixtures of ⁷Li atoms with fermions having the ⁶Li mass.     

T=0 Green's function for the exciton

The excitons as electronic excitations of an insulator are obtained from the full manybody Hamiltonian by means of T=0Green's function techniques. Exciton amplitudes and energies are obtained via the vertex-part equation from an eigenvalue equation which in the Wannier limit is the effective-mass equation. A formula is obtained for the frequency dependent effective interaction whose static limit (ω=0) goes over into the Haken-Schottky dielectric-constant interaction for excitons of large electron-hole separations. A simple criterion will result to answer the question on when one is allowed to replace the frequency dependent interaction by its ω=0 limit.     

Free-energy fluctuations and chaos in the Sherrington-Kirkpatrick model

The sample-to-sample fluctuations Delta FN of the free-energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods. The replica calculation for bond chaos shows that the exponent mu governing the growth of the fluctuations with system size N, Delta FN approximately Nmu, is bounded by mu< or =1/4.     

Electron self-energy effect on a heterojunction bipolar transistor at T=0

An electron self-energy effect on a graded-gap heterojunction bipolar transistor at T=0 is considered. It is found that two competing mechanisms affect the collector current vs. emitter base bias voltage relations: (I) threshold voltage lowering for electron injection from emitter to base improves it: while (II) a decelerating field on injected minority carriers in the base degrades it. In a sufficiently large built-in field in the graded-gap base, negative transconductance appears as a result of the effect (I).