Coarse-graining approach to first-order phase transitions

On an example of a simple spin system with two ground states and no symmetry, we show how to control low-temperature systems near first-order phase transitions by a straightforward renormalization group argument. The method, as opposed to the Pirogov-Sinai approach, also works for complex Hamiltonians.     

Microscopic simulation of the polarization switching at ferroelectric first-order phase transitions

Simulations of the kinetics of polarization switching at first-order ferroelectric phase transitions are carried out within the framework of Ishibashi dipole lattice model. We consider the influence of the dipole–dipole interaction between polar units on the polarization switching taking into account the existence of metastable states. We also examine the size effect on the switching kinetics. We calculate hysteresis loops and switching rates in the systems in which the continuum approximation is not valid. We show that in the case of hundreds of polar units our equations give the known analytical expressions for the switching rate.     

General approach for studying first-order phase transitions at low temperatures

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small T's, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable; an enhanced tempering method, the parallel tempering-accurate for small and intermediate system sizes with rather low computational cost-is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phase density at the coexistence.     

Singularities in first-order phase transitions

Several theories of phase transitions and their inter-relations have been criticized, focusing on the problem of whether z _c, the value of the fugacity corresponding to the point of condensation, is given by z _s, the smallest real positive singularity of the analytic function defined by the power series using volume-independent cluster integrals, or not. The present situation has been analysed and it is made clear that none of the existing theories can give the answer to this problem. Plausibility arguments for an affirmative or negative answer are discussed.     

Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

Weak first-order superfluid-solid quantum phase transitions

We study superfluid-solid zero-temperature transitions in two-dimensional lattice boson-spin models using worm-algorithm Monte Carlo simulations. We observe that such transitions are typically first order with the exception of special high-symmetry points which require fine-tuning in the Hamiltonian parameter space. We present evidence that the superfluid-checkerboard solid and superfluid-valence-bond solid transitions at half-integer filling factor are extremely weak first-order transitions and in small systems can be confused with continuous or high-symmetry points.     

Generalized Gibbs’ approach to the thermodynamics of heterogeneous systems and the kinetics of first-order phase transitions

In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts are widely employed that were developed long ago by Gibbs and van der Waals. However, the results of such analysis are partly unsatisfactory and internally contradictory. By generalizing Gibbs’ approach, the existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of these processes can be developed. The basic ideas of the generalized Gibbs approach and a variety of consequences obtained on its basis with respect to the understanding of the general features of the kinetics of first-order phase transitions are outlined. Dedicated to the memory of Vladimir P. Skripov. The text was submitted by the authors in English.     

Multidimensional kinetic theory of first-order phase transitions

A theory is developed to calculate the steady-state nucleation rate in the multidimensional space of variables describing a nucleus. The nucleation rate, a stationary distribution of nuclei, and the direction of the nucleus flux are calculated within this theory. The expression derived for the nucleation rate is invariant with respect to the dimensionality of the space and includes the result obtained in the one-dimensional theory. The stationary distribution function is expressed in terms of the initial physical variables. The nucleation rate is calculated using a new method that requires neither separation of the variables nor taking into account the symmetry of the diffusion matrix $\hat D$ . However, it is demonstrated that the theory is consistent only if the matrix $\hat D$ is symmetric. The symmetry of this matrix is discussed in relation to the constraints imposed on the direction of the nucleus flux. The normalization of the equilibrium distribution functions is discussed, and the relation between the multi-and one-dimensional theories is shown.     

On the multidimensional theory of the first-order phase transitions

Multidimensional theory of first-order phase transitions in the vicinity of a one-dimensional saddle point is considered. Transformations of the variables describing new-phase nuclei are suggested; these transformations allow one to completely separate the variables in the Fokker-Planck equation and reduce the problem to a one-dimensional one. The distribution function and the nucleation rate are found for both stationary and non-stationary nucleation stages. As an illustration, the problem of boiling of a volatile liquid is considered in the case where new-phase nuclei are characterized by two parameters.