Improved Scaling of the Magnetic Heat Capacity in La<Subscript>0.85</Subscript>Ag<Subscript>0.15</Subscript>MnO<Subscript>3</Subscript> Manganite

The heat capacity in a La_0.8 Ag_0.15 MnO₃ manganite has been measured near the Curie temperature T _C in applied magnetic fields up to 26 kOe to study the scaling critical behavior and to obtain the universality class. The conventional scaling fails in application to the manganites with a hysteresis and the strong sensitivity of T _C to a magnetic field. However, the application of the improved scaling procedure designed by us allows yielding the good scaling the magnetic heat =0.23 capacity in La_0.85Ag_0.15MnO₃, which may belong to a new universality class for systems with the strong spin-orbital coupling of t _2g -electrons, namely, double -Heisenberg with the critical exponent of the heat capacity α = ?0.23 and the critical exponent of the correlation radius v=0.7433. This new universality class is consistent with the crystal, magnetic and orbital symmetries for the La_0.85Ag_0.15MnO₃. Scaling failure in the vicinity of T _C in the range of t/H ^1/2ν ≈ [?0.033;0.024] is understood by finite-size and other disordering effects when T →T _C. It is remarkable that finite-size effect is consistent with grain size, L ≈ 50 μm, in the La_0.85Ag_0.15MnO₃. The correlation radius, Lt ^ν ≈ 30.28 Å, estimated from the finite-size effect is of the same order of magnitude with the sizes of the ferromagnetic fluctuations and drops in manganites.     

Critical properties of the anisotropic Ising model with competing interactions

The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J ₁. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J ₁ is shown to be present in the system.     

Anisotropic finite-size scaling analysis of a two-dimensional driven diffusive system

The standard two-dimensional uniformly driven diffusive model is simulated extensively for much larger systems with a multi-spin coding technique. The nonequilibrium phase transition is analyzed with anisotropic finite-size scaling both at the critical point and off the critical point. The field-theoretic values of critical exponents fit the data well at and aboveT _c . BelowT _c the scaling is rather difficult and the results are not conclusive.     

Magnetic ordering and phase transitions in planar antiferromagnetic systems with a Kagomé lattice

We study the process of magnetic ordering in planar antiferromagnetic systems with a Kagomé lattice. It is found that if the interaction between next-nearest-neighbor spins is taken into account, the heat capacity of such systems has a singularity at a finite temperature T. On the basis of a scaling analysis of finite-size systems we study the behavior of thermodynamic quantities in the neighborhood of a phase transition. We find that the phase transition at the critical point is due to discrete-and continuous-symmetry breaking, in which the long-range chiral order and the power-law translational spin order emerge simultaneously. Finally, we calculate the temperatures of the transition to different (with three and nine spins per unit cell) ordered states. Zh. éksp. Teor. Fiz. 113, 2209–2220 (June 1998)     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

Collapse transition and cyclomatic number distribution of directed lattice animals

We computed the specific heat of directed lattice animals using a Monte Carlo method for various animals sizesN, withN up to 100 on the square andN up to 125 on the simple cubic lattices. The specific heat as a function of the temperature for various animal sizes exhibits peaks which seem to approach a collapse transition temperature monotonically from below with increasingN. A least square fit together with finite-size scaling then gives both the transition temperature T_c and the specific heat exponent for these two lattices. The cyclomatic number distributions for the number of animals with fixed animal sizeN are also calculated and these seem to obey a scaling law for largeN. On leave from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Critical properties of hadronic matter in thermodynamical models

The temperature T₀ in certain thermodynamical models for strongly interacting systems taken as the critical point yields directly the critical exponents for the specific heat and compressibility. We discuss the implications of thermodynamical scaling using various asymptotic conditions.     

Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J ₂/J ₁ in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

     

Computer simulation of the frustrated antiferromagnetic Heisenberg model on a layered triangle lattice

Critical properties of the 3D frustrated Heisenberg model on a triangle latticeare investigated using a replica Monte-Carlo method that considers the interaction between next nearest neighbors. Static magnetic and chiral critical indices for heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation radius ν are calculated using the theory of finite-size scaling.     

Shape dependence of the finite-size scaling limit in a strongly anisotropic $\mathsf{O(\infty)}$ model

We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for numerical finite-size scaling studies of strongly anisotropic systems.Received: 9 April 2003, Published online: 4 August 2003PACS:   05.70.Jk Critical point phenomena - 64.60.-i General studies of phase transitions     

A frustrated heisenberg antiferromagnet on a triangular lattice with next-nearest neighbor interactions

Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation length ν.     

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T _c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems. Received 21 November 2000 and Received in final form 28 February 2001     

Critical behavior of the heat capacity of the manganite La<Subscript>0.87</Subscript>K<Subscript>0.13</Subscript>MnO<Subscript>3</Subscript>

The heat capacity of the manganite La_0.87K_0.13MnO₃ has been measured in the temperature range 80–350 K. The nature of the ferromagnetic phase transition and the critical properties of heat capacity near the Curie temperature have been studied. The regularities of variations in the universal critical parameters near the phase transition point have been established. The calculated critical exponent and amplitudes of the heat capacity with allowance for corrections on the scaling (α = −0.13 and A ⁺/A ⁻ = 1.178) correspond to the critical behavior of the 3D Heizenberg model.     

Phase coexistence and critical point determination in polydisperse fluids

Phase equilibria of fluids with variable size polydispersity have been investigated by means of Monte Carlo simulations. In the models, spherical particles of different additive diameters interact through Lennard-Jones and hard sphere Yukawa intermolecular potentials and the underlying distribution of particle sizes is a Gaussian. The Gibbs ensemble Monte Carlo technique has been applied to determine the phase coexistence far below the critical temperature. Critical points have been estimated by finite-size scaling analysis using histogram reweighting for NpT simulation data. In order to achieve efficient sampling in the vicinity of the critical points, the hyper-parallel tempering scheme has been utilized.     

Thermodynamic properties of multicomponent mixtures near the liquid-vapor critical point

A new method has been proposed to describe the physical properties of multicomponent mixtures near their critical points. The method is based on the transition from the experimental thermodynamic variables to scaling fields, is applicable to a mixture with any number of the components, and is, thus, universal. For the previously studied methane-propane-pentane mixture, it has been shown that the anomalies of the specific heat at a constant volume and derivative (?P/?T)_ρ,x can be quantitatively described in this approach in a wide vicinity of a critical point, including noncritical isochores.     

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.