The zero-distribution of the great partition function in the complex fugacity plane of gases of point particles with logarithmic interaction

The equation of state for gases of point particles with logarithmic interaction is derived. The system exhibits a phase transition at a critical temperature T_c. The critical temperature is a function of the dimension of the system. A hard core must be added below T_c to prevent the system from collapsing. The specific heat diverges on both sides as |T_c - T|^-2 in any dimension.For T≤T_c there are no zeros of the grand partition function in the complex fugacity plane, for T >T_c all zeros occupy the whole negative real axis. The density of zeros will be calculated.     

On the hydrodynamic theory of central peak in displacive structural phase transitions

A model involving nonlinear coupling between the overdamped phonon mode and temperature fluctuations is studied using the dynamic renormalization group method. It is shown that the behavior of the central peak in the dynamic form factor depends on the specific heat exponent α. For α < 0 and as T → T_c the central peak is found to merge with the over-damped phonon mode and the coupling goes to zero at T_c as (T ? T_c)^?α. An argument on the intensity of the central peak in the critical region in presented and it is concluded that the hydrodynamic coupling may not be the dominant mechanism of the central peak in SrTiO₃.     

Phase transition in a linear chain of classical spins with a logarithmic nearest neighbour pair potential

We present the complete calculation of the partition function and correlation functions of a linear array of classical spins coupled by a nearest neighbour logarithmic pair potential. In the case of a ferromagnetic coupling there occurs a phase transition at T_c > 0. The critical exponents of the specific heat C and the magnetic susceptibility χ (in the absence of an external field) are shown to have the non-classical value α = 2 and classical value γ = 1 respectively. The underlying mathematical mechanism of the phase transition is the complete degeneracy of all the eigenvalues of the corresponding integral equation (Kac's mechanism). Below T_c the partition function becomes complex. For antiferromagnetic coupling the free energy is analytic in the whole temperature range and so no phase transition occurs in this case.     

New expression for the partition function of a two-dimentional classical plasma

A new expression is derived for the canonical partition function Q of a two-dimentional Coulomb system. As a by-product Q is shown to exist above the critical temperature T_c for the collapse of a pair of opposite point charges.     

Theory of fluctuations in a network of parallel superconducting wires

We show how the partition function of a network of parallel superconducting wires weakly coupled together by the proximity effect, subjected to a vector potential along the wires, can be mapped onto N-distinguishable two dimensional quantum-mechanics problem with a perpendicular imaginary magnetic field. Then, we show, using a mean field approximation, that, for a given coupling, there is a critical temperature for onset of inter-wire phase coherence. The transition temperature T_c is plotted on both cases for non-magnetic and a magnetic field perpendicular to the wires.     

Critical behaviour of the ising model in a transverse field

A theory for the critical behaviour of the Ising model in a transverse field is presented. The existence of a central component in the spectral density of the longitudinal spin relaxation function is shown to result self-consistently from decay into itself and energy-fluctuation diffusion mode. Estimates of the various quantities are made forT nearT _c , the damping is seen to be temperature dependent. Our theory is appropriate for the caseΓ ～J whereΓ andJ are the magnitudes of the transverse field and the exchange interaction between the spins respectively. Its relevance to neutron scattering data on Van Vleck paramagnets is discussed.     

“Magnetodipole” self-organization of charge carriers in high-T c superconductors and the kinetics of phase transition

A phenomenological model describing “magnetodipole” self-organization of charge carriers (the formation of so-called stripe-structures and the energy gap in the spectrum of states) was suggested to interpret the data of nonstationary nonlinear spectroscopy of high-T _c superconductors. It was shown that, after rapidly heating a superconducting sample, the kinetics of the succeeding phase transition depended on initial temperature T. At small “overheatings” T*<T<T _m x≈(1.4?1.5)T* (T _c and T*≈T _c are the temperatures of the transition to the superconducting state and the formation of stripe-structures) and the optimal level of doping, the decay of stripe-structures (and of the gap in the spectrum of states) occurred at a low rate (in times above to 10^?9 s) in spite of the virtually instantaneous disappearance of superconductivity.     

非线性耗散对亚稳态系统量子衰变速率的影响

发展了一种快速傅里叶变换路径积分方法，研究非线性耗散系统的量子衰变速率，得到了Bounce轨道的作用量S_B，即衰变速率的指数因子.在系统与环境存在非线性耦合f(x)=tanh［λ(x-x_b)］的情形下，发现其对衰变速率具有抑制作用.指数因子随温度T的关系不再满足S_B=a［1-b(T/T_c)²］法则；与通常的线性耗散情形相比，跨越温度T_c回升，即系统更早地进入穿透区域. 关键词： 量子衰变 非线性耦合 路径积分 快速傅里叶变换     

Incoherent tunneling at weak bias: Strong quantum damping

Using a generalized version of Langer's “imaginary part of the free energy” method involving an “extended” bounce and doing a fully “dynamical” evaluation of the weak bias anomalous fluctuation mode, the thermal dependence of the decay rate Γ = A exp(-B) is studied for a metastable quartic potential model in the strong ohmic quantum damping regime in order to extend previous work to a considerably more realistic range of parameters. In particular, the earlier restrictions 12 B exp(-ħω₀/2k_BT)→0 and 2πk_BT/ħω₀→0 are removed. As a consequence there appear - inter alia - T² -corrections in B similar to those occuring for strongly biased metastable systems.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Abnormal properties of spontaneous emission in a Kerr nonlinear blackbody

We reexamine the atomic spontaneous decay in a Kerr nonlinear blackbody by contrast with our previous paper [M. Yin, Z. Cheng, Phys. Rev. A 78 (2008) 063829]. In the process of deriving the atomic decay rate, we use the temperature-dependent velocity of photons to take the full nonlinearity of a KNB into account. It is found that below a transition temperature T_c, the atomic spontaneous emission in a KNB might be enhanced or inhibited compared with that in a normal blackbody whose interior is filled with a nonabsorbing linear medium. The physical origin of the enhancement and inhibition of spontaneous emission is also discussed.     

Phase transition in anyon superconductivity at finite temperature

The magnetic response of the charged anyon fluid at temperatures higher than the fermion energy gap (T ⪢ ω_c) is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration, is found. The inhomogeneity is linked to the existence of an imaginary magnetic mass which increases with the temperature. It is explicitly proved that the electromagnetic field magnetic masses and rest-energies are different in the (T ⪢ ω_c)-phase.     

Exact quantum partition function of the BCS model

The exact calculation of the reduced BCS model quantum partition function (QPF) in the thermodynamic limit is carried out by the path integration method. The expression for the QPF and the phase transition temperatureT _c in the regular phase coincide with the results of Bogolyubov. In the nonregular phase a temperature singularity appears in the expression for the QPF: the QPF diverges in the region of temperaturesT _c which are smaller than some critical temperatureT _c ^* , and it turns out that in all casesT _c ^* > T _c and the differenceT _c ^* –T _c is not small. The interpretation of the temperatureT _c ^* is given.     

19F nuclear magnetic resonance in CeF3

A ¹⁹F pulsed NMR investigation of single crystals of CeF₃ and CaF₂-doped CeF₃ has been undertaken in the temperature range 300–570K at a frequency of 14 and 60 MHz. It was found that the free-induction decay is non-linear and could be fit by a sum of exponentials using a nonlinear least square procedure to an appropriate functional form. The results of this analysis indicate that there are three distinct spin-spin relaxation times T₂, which is consistent with the existence of three inequivalent fluorine sublattices. At room temperature, fluorine ions on two of the sublattices were found to be in motion, with the fastest ion specified as the F3-type in the Oftedal structure.The temperature dependence of the spin-spin relaxation time T₂ for the fastest ions was found to undergo an inversion at 400 and 385K for the pure and doped samples, respectively. The inversion indicates an increase in the interchange rate of ions between two sublattices. Activation energies are 0.29 ± 0.02 eV in the low temperature region and 0.21 ± 0.01 eV in the high temperature region for the pure sample, with corresponding values of 0.24 ± 0.01 eV and 0.23 ± 0.02 eV for the doped sample.T₁ was approximately the same for both samples, and essentially temperature independent, indicating an exchange-dominated spin-lattice decay mechanism.     

The speed of sound in hadronic matter

We calculate the speed of sound c _s in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)～m ^?a exp?{bm}, which leads to singular behavior at the critical temperature T _c =1/b. With a=4 the pressure and the energy density remain finite at T _c , while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near T _c resonance effects dominate, which causes c _s to vanish as (T _c ?T)^1/4. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around T _c , the actual critical behavior in these models is no longer present.     

Anomalous behaviour of GdNi5 near the Curie point

The a.c. permeability and the qualitative behaviour of the electrical resistivity of GdNi₅ have been investigated near the Curie point (T_c). The electrical resistivity shows no unusual properties near T_c but the a.c. permeability exhibits a sharp peak superimposed on the usual relatively slow decay in the transition region. The peak in the susceptibility occurs at 31.8 K in zero external field and may be suppressed by the application of a magnetic field.     

Analyticity of correlation functions for the two-dimensional Ising model

Analyticity of correlation functions for the two-dimensional Ising model as a function of the inverse temperature except for the singularity at the critical temperature is proved. A crucial step is the establishment of the correspondence between extremal equilibrium states of the model and pure ground states of a one-dimensional spin system below the critical temperatureT _c . An exact decay rate of the clustering property along axes is also determined for allTT _c .     

Superconducting phase transitions in ErcY1−cRh4B4

The superconducting transition temperature T_c1 and the reentering temperature T_c2 to the normal ferromagnetically ordered state in the system Er_cY_1?cRh₄B₄ were determined as a function of the concentration of Er. Comparing our results with the recent theory of Maekawa et al., the exchange interactions J′ among local spins and I between local spins and superconducting electrons were estimated as J′ ? 0.30 K and I²N(0) ? 0.046 K, where N(0) is the density of states. A sudden decrease of H_c2 at T_c2 was observed in a high concentration region suggesting the first order transition.     

THE ONE PION EXCHANGE POTENTIAL AT FINITE TEMPERATURE

By means of the imaginary time Greer's function method,we extend the One Pion Exchange Potential (OPEP) of nucleon-nucleon interaction to finite temperature.We sum up all the bubble diagrams and find that the temperature effect to OPEP is small at low temperature region but large at high temperature region.The effective mass of pion field M_π(β) will become imaginary at critical temperature T_c=177MeV.It means that the attractive OPEP will disappear at T_c and the phase transition happens.