The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10^-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given. Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998     

Collapse transition of a two-dimensional lattice animal

The phase diagram and the tricritical point of a collapsing lattice animal are studied through an extended series expansion of the isothermal compressibilityK _T on a square lattice. As a function of the variables of fugacity and Boltzmann weight,K _T is investigated using partial differential approximant techniques. The characteristic flow pattern of partial differential approximant trajectories is determined for a stable fixed point. We obtain satisfactory estimates for the tricritical fugacityx _t =0.024±0.005 and temperatureT _t =0.54±0.04. Taking into account only linear scaling fields, we are also able to get the scaling exponent =1.4±0.2 and the crossover =0.66±0.08. Our results are in reasonable agreement with previous estimates in the literature.     

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 horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T _c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T _c decay algebraically with critical exponent =1/4 and exponentially forT>T _c. 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 =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln     

EuPtP: a new mixed valent europium-system

The europium valency in hexagonal EuPtP, as examined byL _III-x-ray absorption and Moessbauer experiments, is a function of temperature and changes from 2.16 at 295 K to 2.40 at 4 K. In the region of the strongest temperature dependence of the valency, the compound undergoes two first order phase transitions atT ₁=235 K andT ₂=190 K, characterized by discontinuities in the lattice constants and in the magnetic susceptibility. In the europium Moessbauer spectra, several temperature dependent absorption lines were found, indicating a complex europium valency behaviour. Furthermore, we observe antiferromagnetic order at 8.6 K.Supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 125Supported by Deutsche Forschungsgemeinschaft     

4f-electric quadrupolar effects on the lattice constants and magnetism of RCu2Ge2 (R=rare-earths)

The temperature dependence of the lattice constants of the alloys, RCu₂Ge₂ (R=Nd, Tb, Dy, Ho and Tm) shows the existence of a lattice strain due to the alignment of the 4f-electric quadrupole at low temperatures. This strain could be related to the deviation of the Néel temperatures (T _N ) from that predicted by de Gennes scaling, thereby indicating the role of the quadrupole on the magnetism. On the other hand, in PrCu₂Ge₂, for which the enhancement ofT _N is the largest in thisR series, the lattice constants interestingly behave as if the 4f-quadrupole moment is almost quenched and the anomalous magnetism in this case is attributed to some degree of 4f-delocalisation.     

A note on mean-field behavior for self-avoiding walk on branching planes

We consider the critical behavior of the susceptibility of the self-avoiding walk on the graphT×Z, whereT is a Bethe lattice with degreek andZ is the one dimensional lattice. By directly estimating the two-point function using a method of Grimmett and Newman, we show that the bubble condition is satisfied whenk>2, and therefore the critical exponent associated with the susceptibility equals 1.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Magnetic Phase Transitions in CePtSn

CePtSn, crystallizing in the orthorhombic TiNiSi-type structure, exhibits two antiferromagnetic transitions at T _N=7.8 K and T _M=5.2 K. Low-temperature X-ray diffraction study has been done to investigate changes in lattice parameters connected with these magnetic phase transitions. Specific-heat data in the same temperature region are also presented. Magnetization isotherms at T>T _N up to 14 T have been measured and the obtained results are compared with theoretical calculations based on a microscopic model Hamiltonian.     

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.     

Ising models on the pentagon lattice

We solve inhomogeneous Ising models on the pentagon lattice using the transfer matrix formalism. As two special cases we study the ferromagnetic and the fully frustrated antiferromagnetic model on this lattice. The ferromagnet shows a phase transition at someT _c>0 with the usual Ising behaviour. In the frustrated case no transition occurs at any temperature due to frustration. Frustration also causes a nonvanishing rest entropy. We also calculate the spin-spin-correlation for large distance in both cases. In the ferromagnetic model we thus get the magnetization and the expected algebraic (exponential) decay of the correlations at (above)T _c. The correlations of the frustrated model decay exponentially for all temperatures, includingT=0, indicating that evenT=0 belongs to the disordered high temperature phase. Superimposed to the exponential decay the correlation shows an interesting oscillatory behaviour with temperature dependent wave number, i.e. an incommensurate structure.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.     

二维完全阻挫$lt;i$gt;XY$lt;/i$gt;模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless（KT）型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上（T>T_KT）,独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下（T<T_KT）测量的结果一致. 关键词： 蒙特卡罗法 动力学指数 Kosterlitz-Thouless相变 XY模型')" href="#">二维完全阻挫XY模型     

Thermodynamical properties and defect energetics of an n-body potential adapted to Cu3Au

By using molecular statics, molecular dynamics, and Monte Carlo techniques we validate a previously developed empirical n-body potential adapted to Cu₃Au. At T=0 K, predicted cohesive energies, lattice parameters, and elastic constants in CuAu and CuAu₃ as well as the formation energy of vacancies in Cu₃Au are in good agreement with experimental data. A satisfactory behavior is also obtained at T 0 K in Cu₃Au, for atomic mean-square displacements and elastic moduli. However, this model underestimates the vacancy migration energy and the order-disorder critical temperature when the latter is evaluated by Monte Carlo including both exchanges between atoms of different species and atomic moves simulating vibrations.     

双层钙钛矿La1.8Ca1.2Mn2O7磁性相关I-V非线性与电输运性质

采用传统固相反应法制备了双层钙钛矿结构锰氧化物La_1.8Ca_1.2Mn₂O₇陶瓷,并用X射线粉末衍射法,扫描电镜,HL5500PC Hall效应分析仪和综合物性测量系统(PPMS)对其磁、电性质进行了表征.结果表明:经过两次高温烧结可合成具有双层Sr₃Ti₂O₇型四方结构的La_1.8Ca_1.2Mn_2<     

Unified study of lead: Energy-dependent pseudopotential calculation

A Unified study of lattice-mechanical properties of lead using energy-dependent pseudopotential is carried out. Energy dependence in pseudopotential is considered through the effective mass approximation; the pseudopotential model chosen is the local Heine-Abarenkov model potential. Properties studied include cohesive energy, equilibrium lattice parameter, second-order elastic constants, pressure derivative of second-order elastic constants, equation of state (atT=0 K), phonon-dispersion and effective two-body interaction. The results show fairly good agreement with experiment especially with a modified Heine-Abarenkov potential.     

Normal-state and superconducting properties of HfV2

We present experimental results for the low-temperature specific heat, electrical resistivity, elastic constants, ultrasonic attenuation and thermal conductivity of theC 15 Laves phase HfV₂ for both polycrystalline and single crystal samples. BelowT _c =9 K, the temperature dependence of the specific heat can roughly be approximated by aT ³ law over a large temperature range. This may be explained with strong coupling effects in consistence with the high value for C/T _c =1.9. Heat transport appears dominated by the known phonon contribution also belowT _c . There is no electronic contribution to the ultrasonic attenuation in HfV₂.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Scaling of particle trajectories on a lattice

The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. On both lattices, for most concentrations of the scatterers the trajectories close exponentially fast. For special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters.At criticality, in addition to the two critical exponents =15/7 andd _f=7/4 found before, the critical exponent =3/7 appears. This exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity. New scaling behavior was found for the square lattice partially occupied by rotators, indicating a different universality class than that of percolation clusters.Near criticality, in the critical region, two scaling functions were determined numerically:f(x), related to the trajectory length (S) distributionn _s, andh(x), related to the trajectory sizeR _s (gyration radius) distribution, respectively. The scaling functionf(x) is in most cases found to be a symmetric double Gaussian with the same characteristic size exponent =0.433/7 as at criticality, leading to a stretched exponential dependence ofn _S onS, n_Sexp(–S ^6/7). However, for the rotator model on the partially occupied square lattice an alternative scaling function is found, leading to a new exponent =1.6±0.3 and a superexponential dependence ofn _S onS.h(x) is essentially a constant, which depends on the type of lattice and the concentration of the scatterers. The appearance of the same exponent =3/7 at and near a critical point is discussed.     

Critical exponents of Manhattan Hamiltonian walks in two dimensions,from Potts andO(n) models

We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq ^1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model in the low-temperature phase withn =q ^1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < T_c), corresponding to a conformal theory with central chargeC = –2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.     

Magnetic studies on RCo3B2 (R=Sm,Gd, Er)

Compounds RCo₃B₂ withR=Sm, Gd, and Er were prepared and identified structurally by X-ray diffraction. Magnetic properties of these materials were studied down to liquid He temperature. The materials order ferromagnetically (e.g.,T _c for GdCo₃B₂ is 58 K). The magnitude of saturation moments indicates that Co is nonmagnetic in this environment. Bulk specimens of the compound SmCo₃B₂ show extraordinarily high coercive forces at 4.2 K (H _c =50 kOe). The second-order crystal field term of Sm in this compound is calculated on the point charge crystal field model and is found to be considerably larger than the one of Sm in SmCo₅. This is mainly due to the unusual ratio of the lattice constants. This work was supported by a grant from the National Science Fundation.     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999