Static and dynamic correlation functions of a Landau-Ginzburg model near the magnetization curve

A recently developed method for treating static Goldstone modes is extended to the dynamics of purely dissipative Landau-Ginzburg models. The extension hinges on the existence of fluctuation-dissipation relations which closely link the dynamic and the static problem. This connection, and previous work on the static problem, suggest that a perturbative approach to the dynamic Goldstone singularities should be possible. We present such a perturbation theory. For a nonconserved order parameter we show to two loop order that our approach is internally consistent. We give approximate expressions for both static and dynamic correlation functions in the whole critical region, including the magnetization curve.     

Scaling function for the energy density correlation at large momentum

The static energy-density correlation function S ²(0)S ²(x)–S ²² is calculated in the critical region for theS ⁴ Ginzburg-Landau-Wilson model at short distances and for nonzero field. Short distance expansion is used and its structure for more complex vertex functions is given. Goldstone mode singularities present at the magnetization curve are taken into account. The main application is given in the theory of polymer solutions. Here, S ²(0)S ²(x)–S ²² becomes the Fourier transform of the densitydensity correlation.     

Multifractal magnetization on hierarchical lattices

A new approach is applied to show that the local magnetization of the ferromagnetic Ising model on hierarchical lattices has a multifractal structure at the critical point. Thef() function characterizing its multifractality is presented and discussed for the diamond hierarchical lattice. Distinct exact critical exponents for the average magnetization and for the local magnetization of the deepest sites are found. The average magnetization (as function of the temperature) is also calculated. The critical exponent of the susceptibility is estimated using finite-size scale arguments.     

Domain wall instability in biaxial ferromagnets

The energetic and dynamic stability of domain walls (DW's) in a 1D Heisenberg ferromagnet with orthorhombic anisotropy is examined in the framework of classical continuum theory. It is shown that in the undamped chain the critical slowing-down accompanying the energetic instability of the static DW's at a critical ratioa _c of the anisotropy fields is not marked (as one might expect) by a localized soft dynamic mode of the DW's, but it is realized by a mechanism which may be termed softening of the velocity change. The role of the soft eigenmode is taken over by the perturbation which carries the static DW into a moving one with infinitesimal velocity, and the role of the soft-mode frequency is taken over by the velocity change induced by the perturbation. When spin damping is included, one does find a soft relaxation mode: Attenuation of the velocity of moving DW's gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. This behaviour is not a special feature of the system under consideration, but a similar situation arises in general, when a static DW becomes unstable with respect to a perturbation connecting it with a family of other static DW's. For moving DW's the softening of the velocity change also occurs, but here no energetic stability criterion is available and inclusion of spin damping makes the DW motion nonstationary. Thus, in the case of moving DW's no possibility seems to exist to define stability and instability in the usual terms of linear analysis.Work supported by the Swiss National Science Foundation     

New approaches inμ + SR studies on critical phenomena in Ni

The critical phenomena in Ni are probed by pulsedSR method under longitudinal- and zero external magnetic fields. The sample magnetization around the critical temperature is confirmed simultaneously by bulk magnetization measurement in situ, disappearance of transverseSR signal and recovery of asymmetry under longitudinal field. At the same time, the ratio of the ⁺ hyperfine field to the bulk magnetization in the ferromagnetic phase below the critical temperature is determined from the observables obtained only in the present experiment. The zero- and low-field longitudinal relaxation rate of muon does not diverge in approaching toT _c in the paramagnetic region, but seems to reach a saturation value.This work is supported by the Grand-in-Aid of the Japanese Ministry of Education, Culture and Science.     

Finite size effects and spontaneously broken symmetries: the case of theO(4) model

Finite volume numerical simulations of scalar models with continuous symmetry face strong finite size effects in the broken phase due to the presence of light Goldstone states. In the region where the light Goldstone bosons dominate the dynamics of the system universal finite size scaling formulae are predicted by chiral perturbation theory. Introducing a finite external source one can determine infinite volume, zero external source physical quantities from finite volume observables. Here we apply this theoretically controlled approach to the 4 dimensionalO(4) scalar model. All of our numerical results are in excellent agreement with the predicted finite size scaling forms. We confirm earlier results at zero external source where the infinite volume limit was approximated by projecting the fields to the direction of the magnetization.     

Investigation of the critical properties of the three-dimensional weakly diluted potts model

The problem of the type of the phase transition in the three-dimensional weakly diluted Potts model with the number of spin states q= 3 has been investigated by the Monte Carlo method. The temperature dependences of the Binder cumulants, energy, magnetization, specific heat, and susceptibility have been calculated. It is found that the second-order phase transition occurs in a system at the spin concentration p = 0.9. The critical exponents of the magnetization (β), specific heat (α), and susceptibility (γ) and the critical correlation-length exponent v were calculated on the basis of the finite-size scaling theory at p = 0.9.     

Ground state of a spin-phonon system. III. Small-B limit

The ground state of the spin-one-half acoustic phonon system is studied in the limitB1. The technique is to combine the Brillouin-Wigner variational perturbation theory with a source canonical transformation. With theB=0 source transform the energy is calculated as a function of coupling constant through terms of orderB ². To this order there is no phase transition. The theory gives the crossover from perturbation theory to an improved classical theory with quantum fluctuations. With a source transform with a nonzero inverse length the energy estimate is further improved to next order in the coupling constant and for larger values ofB. The soft, infinite-order transition of the modified source theory is removed in the limitB1.     

The magnetization-energy scaling limit in high dimension

In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimensiond exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the bubble quantity.On leave from the University of Arizona, Tucson, Arizona 85721.     

Constrained variational problem with applications to the Ising model

We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (–)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical valueB ₀ (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a squeezed Wulff shape. The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.     

Motion of vortex lines and mutual friction in superfluid4He nearT λ

The motion of a single vortex line in superfluid⁴He nearT is studied within modelF. The linear response of the vortex-line velocityv _L to a homogeneous counterflowv _s –v _n is calculated up to lowest order of renormalized perturbation theory. The critical temperature dependence is taken into account via the renormalizationgroup theory. Non-asymptotic critical effects are found to be important. The results are generalized to describe collective vortex motion and mutual friction in rotating superfluid⁴He. The phenomenological mutual-friction coefficientsB andB of Hall and Vinen are determined without adjustment of parameters. ForB quantitative agreement with experiments nearT is found whereas forB the agreement is only semiquantiative.     

Novel magnetic properties of the Hubbard chain with an attractive interaction

The magnetic properties of an attractive Hubbard chain are considered. Based on the Bethe Ansatz equations of the problem, exact analytic expressions are derived for the magnetization and susceptibility. These formulae can be evaluated after solving certain derivatives of the Bethe Ansatz equations. These derivative equations are also given. We give the magnetization and susceptibility curves for several values of the interaction-strength and bandfilling. We find that the susceptibility at the onset of magnetization (at the critical field) isfinite for all bandfillings, except for the cases of half filled and empty bands, and in the limit of vanishing interaction. We argue that the finiteness of the initial susceptibility is due to the fermion-like behavior of the bound pairs. We also give the gap (what is equal to the critical field) and the initial susceptibility as functions of the interaction-strength and bandfilling for the cases of nearly half filled and almost empty bands as a function of the interaction, and in the weak coupling limit as a function of the bandfilling. To our knowledge, this is the first Bethe Ansatz calculation for the gap in this latter limit.     

Bethe-Ansatz solution of the ground-state of theSU (2j+1) Kondo (Coqblin-Schrieffer) model: Magnetization,magnetoresistance and universality

The magnetization, the magnetoresistance and the populations of the spin components of the Coqblin-Schrieffer model forj5/2 are calculated from the Kondo limit of a mixed-valence model discussed previously. The results forj=1/2 andj=1 agree with those given in the literature. Forj3/2 only an approximate solution of the integral equations is given, which interpolates between the exact low and high-field results. The universality is discussed and the exact Wilson-numbers are obtained. The Kondo limit of the mixed-valent model is shown to be equivalent to the Coqblin-Schrieffer model by using the Bethe-ansatz equations.     

The ground state properties of the He4-nucleus

Conclusions Table VIII summarizes the computed binding energy of He⁴-nucleus which includes the zeroth order contribution and the correction up to the third order for three different potentials. The binding energy does not contain the C.M. energy, which has been calculated up to the second order. The r.m.s. radii corrected for the C.M. motion and for not-point-like nucleons are calculated up to the second order for potential RHEL 1 and up to the first order for Reid and RHEL 2 potentials. The binding energy and r.m.s. radii are computed for two different self-consistent conditions, the first of which is the usual classical condition (2.16), the second reads E ⁽¹⁾ = 0.In all cases the absolute value of the binding energy of the He⁴-nucleus is lower than the experimental value.It has been shown that the perturbation series built up on the Goldstone reaction matrix diverges, when a self-consistent technique is not used. This represents certain danger also for the self-consistent formulation, although it gives plausible results up to the third order. The result obtained seems to indicate that the discrepancy between the experimental and theoretical values for the binding energy may be caused by neglect of some fundamental facts (relativistic effects, many-body forces etc.) in the present many-body theory.The authors would like to thank the Rutherford High Energy Laboratory for the help in performing necessary computations and for the encouraging interest in this problem.     

On the spontaneous magnetization in the Ising model

The equality between the spontaneous magnetization and the long range order is established for the Ising model with nearest neighbour interactions for low and high temperatures. The proof is presented for the two-dimensional lattice but works also in higher dimensions. The result verifies that the valuem*=(1–(Sh)^–4)^1/8 of the spontaneous magnetization below the critical point calculated by Onsager and Yang is the true value, which has been a long standing open question.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Dynamics of non-linear systems: The kink-phonon interaction

The interaction between non-linear elementary excitations (kinks) and phonons is examined, within the context of perturbation theory previously developed by Hasenfratz and Klein, for the case of the ⁴-model. It is demonstrated that the effect of a kink-phonon collision will be a shift in the kink's position, for which an analytical expression is given. It is conjectured that, as thermal phonons collide with the kink, the latter performs a purely diffusive motion. An estimate of the kink diffusion constant is given, based on a simple kinetic theory of kink-phonon collisions. The light scattering spectrum of a gas of non-interacting moving kinks with a thermal velocity distribution function is calculated; a central peak is found, whose structure reflects the kinks' diffusion.     

Perturbation foundation of <Emphasis Type="Italic">q</Emphasis>-deformed dynamics

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians; one originates from the perturbation expansion of the potential in one configuration space, the other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved. The first is Equivalence Theorem I: Perturbation expressions of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. The general Equivalence Theorem II is: for any potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied. Received: 6 September 2002 / Revised version: 21 October 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: jzzhang@physik.uni-kl.de, jzzhang@ecust.edu.cn     

The spontaneous generation of magnetic fields at high temperature in a supersymmetric theory

The spontaneous generation of magnetic and chromomagnetic fields at high temperature in the minimal supersymmetric standard model is investigated. The consistent effective potential including the one-loop and the daisy diagrams of all bosons and fermions is calculated and the magnetization of the vacuum is observed. The mixing of the generated fields due to the quark and s-quark loop diagrams and the role of superpartners are studied in detail. It is found that the contribution of these diagrams increases the magnetic and chromomagnetic field strengths as compared with the case of a separate generation of fields. The magnetized vacuum state is found to be stable due to the magnetic masses of gauge fields included in the daisy diagrams. Applications of the results obtained are discussed. A comparison with the standard model case is given. Received: 18 October 2002 / Revised version: 23 December 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: vadimdi@yahoo.com RID="b" ID="b" e-mail: skalozub@ff.dsu.dp.ua     

On the dynamics of phase separation

A new framework is developed for a treatment of the unmixing of an alloy or another system undergoing a phase transition after a quench into the coexistence region. Expanding around a suitably chosen reference equilibrium state new order parameter fields are introduced by a regrouping of diagrams. In a path integral representation the action of the new fields is constructed in a renormalized form and calculated by expansion ind=4– dimensions. As a first application the timedependence of the structure factor is computed using a simple factorization. It is found that unmixing takes place in the whole coexistence régime with a lifetime of metastable states which diverges at the coexistence curve and with no sharp boundary between the spinodale and nucleation régime.