Absence of first-order phase transitions for antiferromagnetic systems

We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.     

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.     

Critical-exponent renormalization and first-order transitions

The critical behaviour of systems with short-range interactions in which the free energy has divergent second derivatives is shown to be unstable under small perturbations of e.g. long-range nature. In general there will be critical-exponent renormalization or first-order transitions.     

Studies on magnetic-field-induced first-order transitions

We shall discuss magnetization and transport measurements in materials exhibiting a broad first-order transition. The phase transitions would be caused by varying magnetic field as well as temperature, and we concentrate on ferro- to antiferromagnetic transitions in magnetic materials. We distinguish between metastable supercooled phases and metastable glassy phase.     

Finite-size effects at first-order transitions

Finite-size rounding of a first-order phase transition is studied in “block”- and “cylinder”-shaped ferromagnetic scalar spin systems. Crossover in shape is investigated and the universal form of the rounded susceptibility peak is obtained. Scaling forms on the low-temperature side of the critical point are considered both above and below the borderline dimensionality,d _>=4. A method of phenomenological renormalization, applicable to both odd and even field derivatives, is suggested and used to estimate universal amplitudes for two-dimensional Ising models atT=T_c.     

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.     

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.     

Crossover finite-size scaling at first-order transitions

In a recent paper we developed a method which allows one to control rigorously the finite-size behavior in long cylinders near first-order phase transitions at low temperature. Here we apply this method to asymmetric transitions with two competing phases, and to theq-state Potts model as a typical model of a temperature-driven transition, whereq low-temperature phases compete with one high-temperature phase. We obtain the finite-size scaling of the firstN eigenvalues (whereN is the number of competing phases) of the transfer matrix in a periodic box of volumeL × ... ×L ×t, and, as a corollary, the finite-size scaling of the shape of the order parameter in a hypercubic box (t=L), the infinite cylinder (t=), and the crossover regime from hypercubic to cylindrical scaling. For the two-phase case (N=2 we find that the crossover length _L is given by O(L^w)exp(L^v), where is the inverse temperature, is the surface tension, and w=1/2 if v+1=2 whilew=0 if v+1 >2. For the standard Ising model we also consider free boundary conditions, showing that _L=exp[L^v+O(L^v– 1)] for any dimension v+12. For v+1=2 we finally discuss a class of boundary conditions which interpolate between free (corresponding to the interpolating parameter g=0) and periodic boundary conditions (corresponding to g=1), finding that _L=O(L^w)exp(L ^v) withw=0 forg=0 andw=1/2 for 0<g1.     

Properties of ferroelectric thin films with a first-order phase transitions

A Green's function technique is used to investigate the properties of ferroelectric thin films with a first-order phase transitions on the basis of the transverse Ising model. Taking into account the four-spin interactions beside the two-spin interactions the dependence of the polarization on film thickness and temperature and the thickness dependence of the Curie temperature become more complicated.     

On the possibility of fluctuation-driven first-order transitions

Available experimental material on phase-transitions of cubic compounds to type I- or type II-antiferromagnetism is briefly reviewed. Particular emphasis is paid to the question of whether they exhibit fluctuation-driven discontinuous transitions as claimed by a series of renormalization-group (RG) investigations for order-parameters withn4 degrees of freedom. It turns out that only less than one quarter of the known transitions are classified to be of first order. For most of these, the dominant spin-lattice couplings, i.e. exchangestriction of 3d-ions and magnetostriction and quadrupole-quadrupole interaction forf-ions, are known from independent experiments. Taking this into account, the discontinuous behaviour of the order parameter and related thermodynamic properties were fully explained neglecting critical fluctuations, i.e. by mean-field or randomphase approximations. In the remaining systems, the discontinuity predicted by the RG is not observed, for which several reasons may be responsible: (i) extremely small jumps of the order parameter that are below the limits of experimental resolution or are smeared out by imperfections, (ii) compounds with small spin-lattice interactions may exhibit an-K instead of a single-K structure postulated by the RG-work, and (iii) failure of the RG-criteria established at four dimensions for first-order transitions of readd=3 magnets.     

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.     

Supercooling across first-order phase transitions in vortex matter

Hysteresis in cycling through first-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature T or magnetic field H (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in H-T space, and will be larger when T is lowered at constant H compared to the case when H is lowered at constant T. We discuss the effect of isothermal field variations on metastable supercooled states produced by field-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.