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.     

Induced moment antiferromagnet in an external magnetic field—I: Molecular field theory

The behavior of a two-level induced moment antiferromagnet in an external magnetic field is investigated in the molecular field approximation. A significant reduction in the critical field and in the sublattice magnetizations is shown. However, the total magnetization rises more rapidly with field and can remain at large value in an external field even at T = 0. The magnetic susceptibility also remains finite at T = 0 in contrast to the case of a permanent moment Ising antiferromagnet. The effects of a ferromagnetic next-nearest neighbor interaction are then examined. It is shown that, in contrast to the usual Ising antiferromagnets, the ferromagnetic coupling has to exceed a certain value depending on the crystal field strength and the antiferromagnetic interaction, to allow for a first order phase transition in a field to occur even at zero temperature.     

Specific heat of one-dimensional S = 1 system

Calculations of the specific heat are presented for the one-dimensional S = 1 system in zero external field, using an extrapolation of results for finite rings and chains.     

Thermodynamic properties of the XXZ double chain with long-range interactions

Using the Jordan-Wigner transformation and cut-off approximation, the Letter studies the one-dimensional spin-1/2 XXZ double chain with z-directional uniform long-range interactions in the external magnetic field. Thermodynamic properties as the Helmholtz free energy, internal energy, specific heat and magnetization of the system are obtained. The first and second-order phase transition of the system at a finite temperature are also given. Our results agree with those of the other literatures.     

Existence of the S-matrix in quantum field theory in curved space-time

The existence of the S-matrix is proven for particle creation by an external gravitational field of compact support. No infrared divergences occur even for massless quantum fields; in particular, a localized gravitational field always produces a finite expected total number of particles. The results of this paper apply to both boson and fermion fields as well as to more general linear, external potential interactions.     

The functional renormalization group and O(4) scaling

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale-dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. We perform a set of approximations to formulate and solve the FRG flow equation in the presence of fermionic degrees of freedom and test their influence on the O(4) critical properties expected in the quark-meson model. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed for vanishing baryon density. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom–Griffiths form of the magnetic equation of state, obtained by a systematic ε expansion of the scaling function.     

Monte Carlo study of three-dimensional QCD at finite temperature

Three-dimensional QCD at finite temperature is analyzed using Monte Carlo calculations. It is shown that confinement at low temperature is lost through a second-order phase transition. At high temperature, static quarks are liberated and screened and it is argued that timelike (A₀) gluons are liberated. Just above the critical temperature electric correlation functions seem to be dominated by a resonance of two timelike gluons, whose existence is suggested by perturbation theory. The influence of an external magnetic field close to the critical point is considered.     

Temperature and magnetic field dependence of the absorption edge and the conduction band width of ferromagnetic semiconductors

We investigate the shift of the absorption edge and the behaviour of the conduction band width of ferromagnetic semiconductors as functions of temperature T and an external field B, respectively. Numerical results are given for EuO and EuS. As a consequence of electron-magnon scattering processes the band width of EuO is enhanced by more than 14% in the temperature region: 40 K…T…80 K. The external field tries to surpress this effect.     

Properties of an adiabatically cooled SK spin glass

Some physical properties of an SK spin glass subject to slow cooling are investigated. Among those are Edwards-Anderson order parameter, energy, field cooled and zero field cooled susceptibilities. The results are compared with predictions from Parisi's solution. Different values are obtained for the field cooled susceptibility whereas other quantities are identical in both calculations. Ultrametricity results in a natural way if adiabatic temperature changes involving cooling and heating periods are considered. Some results are also given for adiabatic cooling in a finite external field and for adiabatic changes of the field at constant temperature. The present setup allows to investigate explicitly the dependence on history at least for adiabatic changes of temperature and external field.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Survival of charged ρ condensation at high temperature and density

The charged vector ρ mesons in the presence of external magnetic fields at finite temperature T and chemical potential μ have been investigated in the framework of the Nambu-Jona-Lasinio model.We compute the masses of charged ρ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential.The self-energy of the ρ meson contains the quark-loop contribution,i.e.the leading order contribution in 1/N_C expansion.The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eB_c,which indicates that the charged vector meson condensation,i.e.the electromagnetic superconductor can be induced above the critical magnetic field.Surprisingly,it is found that the charged ρ condensation can even survive at high temperature and density.At zero temperature,the critical magnetic field just increases slightly with the chemical potential,which indicates that charged ρ condensation might occur inside compact stars.At zero density,in the temperature range 0.2 — 0.5 GeV,the critical magnetic field for charged ρ condensation is in the range of 0.2 — 0.6 GeV~2,which indicates that a high temperature electromagnetic superconductor might be created at LHC.     

Nonequilibrium second-order phase transitions in stochastic lattice systems: A finite-size scaling analysis in two dimensions

Two-dimensional lattice-gas models with attractive interactions and particleconserving happing dynamics under the influence of a very large external electric field along a principal axis are studied in the case of a critical density. A finite-size scaling analysis allows the evaluation of critical indexes for the infinite system asβ=0.230±0.003,v=0.55±0.2, and α 0. We also describe some qualitative features of the system evolution and the existence of certain anisotropic order even well above the critical temperature in the case of finite lattices.     

Sudden transition from finite temperature spin environments

We investigate the phenomenon of sudden transition from finite temperature critical environments in the study of quantum correlations of a two-qubit system coupled to independent thermal Ising baths. The influence of the temperature and external field of bath on the critical time of sudden transition is also explored. It is found that the phenomenon of sudden transition can be used to detect the critical points of thermal spin environments. How to protect quantum correlations of the system is also examined by applying a series of π-phase pulses.     

Mössbauer study of the magnetic structure of FeP

The compound FeP shows, at low temperatures and in zero external magnetic field, a helical spin configuration for iron with a propagation vector along the c-axis as deduced from neutron diffraction studies. We have performed ⁵⁷Fe Mössbauer measurements in the temperature interval between 295 K and 4.2 K and in an external magnetic field on both powder specimen and single crystals of FeP. The results show a nearly temperature independent electric quadrupole interaction strength eQV_zz of 1.34 mm/s and a Néel temperature of 115 K. It was, however, impossible to fit the Mössbauer spectra below T_N using a simple double spiral model. Instead a bunched spiral model with the spins crowded along the a-axis gave very good fits. The magnetic hyperfine field was furthermore found to be modulated in the ab-plane. The maximum field of +3.6 T was found along the a-direction while the overall field, presumably spread over all other directions, was 0.2 T. The measurements in external magnetic field showed that the grains become partially oriented with the basal plane parallel to the external field.     

Magnetic field penetration into a 3D ordered Josephson medium and applicability of the bean model

The results of calculation of penetration of an external magnetic field into a 3D ordered Josephson medium, based on analysis of modification of the configuration in the direction of the decrease in its Gibbs potential, are reported. When the external field slightly exceeds the stability threshold, the Meissner configuration is transformed into a periodic sequence of linear vortices, which are parallel to the boundary of the medium and are located at a certain distance from it. There exists a critical value I _C separating two possible regimes of penetration of the external magnetic field into the medium. For I > I _C , for any value of the external field, a finite-length boundary current configuration appears, which completely compensates the external field in the bulk of the sample. At the sample boundary, the field decreases with increasing depth almost linearly. The values of the slope of the magnetic field dependence are rational fractions, which remain constant in finite intervals of I. When the value of I exceeds the upper boundary of such an interval, the slope increases and assumes the value of another rational fraction. If, however, I < I _C , such a situation takes place only up to a certain value of external field H _max. For higher values, the field penetrates into the medium to an infinite depth. These results lead to the conclusion that the Bean assumptions are violated and that Bean’s model is inapplicable for analyzing the processes considered here.     

The quantum acoustomagnetoelectric field in a quantum well with a parabolic potential

The acoustomagnetoelectric (AME) field in a quantum well with a parabolic potential (QWPP) has been studied in the presence of an external magnetic field. The analytic expression for the AME field in the QWPP is obtained by using the quantum kinetic equation for the distribution function of electrons interacting with external phonons. The dependence of the AME field on the temperature T of the system, the wavenumber q of the acoustic wave and external magnetic field B for the specific AlAs/GaAs/AlAs is achieved by using a numerical method. The problem is considered for both cases: The weak magnetic field region and the quantized magnetic field region. The results are compared with those for normal bulk semiconductor and superlattices to show the differences, and we use the quantum theory to calculate the AME field in the QWPP.     

Magnetic properties of (NdxY1-x)Co2(1⩾ x ⩾ 0)

The concentration dependence of T_c and T_R (T_c magnetic ordering temperature, T_R spin reorientation temperature) of the pseudobinary system (Nd, Y)Co₂ is reported. Furthermore the influence of an external magnetic field on the spin reorientation and the magnetization is studied. The observed variation of the magnetization in the vicinity of the spin reorientation is compared with theoretical results. For the calculation a Hamiltonian with terms describing a molecular field, a cubic crystal field, and an external field is used.     

Discrete temperatures in high-temperature superconductors

The low-amplitude AC susceptibility on intact and deformed Bi2223/Ag tapes has been measured as a function of temperature, frequency, AC amplitude and DC magnetic field. The deformation resulted in the splitting of the χ″(T) peak into three peaks situated near 30, 58 and 90 K. In zero magnetic field, these temperatures were identified as the Kosterlitz–Thouless transition temperatures of low number stacks of superconducting layers. An external magnetic field redistributed the dissipation among the peaks, and moved them to lower temperatures (and suppressed the highest temperature peak). In a finite field, each peak corresponds to the stack melting temperature T_m. The melting temperature in each stack was found to be a field-dependent parameter, with a minimum value=T_KT of a stack of thickness that is less by one layer. The T_m decreases exponentially with the field, and the rate of decrease depends on the interstack Josephson and magnetic interactions. With a universal set of T_KT, the vortex melting line of a tape is a linear combination of the T_m(H) for the low-number stacks.     

Out-of-equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry-broken λ(Φ ²)² scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J→ - J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken λ(Φ ²)² scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.     

Zero energy and thermodynamic equilibrium

Using path integral techniques, it is shown that the real time formalism for finite temperature field theory requires an extra Feynman rule for Feynman diagrams carrying zero-external energies. This is related to a general principle governing the use of equilibrium finite temperature field theory. It is shown that only with this extra Feynman rule does the real time formalism become consistent for zero energy calculations. It is also used to understand the problem of the lack of analyticity at zero external four-momenta encountered in finite temperature field theory diagrams.