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.     

Fluctuation-driven quantum phase transitions in clean itinerant ferromagnets

The quantum phase transition in clean itinerant ferromagnets is analyzed. It is shown that soft particle-hole modes invalidate Hertz's mean-field theory for d< or =3. A renormalized mean-field theory predicts a fluctuation-induced first order transition for 1相似文献   

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.     

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.     

Mean field theory of dynamic phase transitions in ferromagnets

We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H_b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H_b)-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.     

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.     

Surface induced disordering at first-order bulk transitions

Semi-infinite systems may undergo surface induced disordering transitions. These transitions exhibit both critical surface behaviour and interface delocalization phenomena. As a consequence, various surface exponents can be defined although there are no bulk exponents. It is shown that the corresponding power laws can be derived from a scaling form for the surface free energy where two independent surface exponentsΔ ₁ and α _s enter. In addition, global phase diagrams with finite symmetry breaking fields are also briefly discussed.     

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.     

Driving rate effects in avalanche-mediated first-order phase transitions

We study the driving-rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behavior emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We confirm our findings by numerical simulations of a prototype model.     

Surface-induced finite-size effects for first-order phase transitions

We consider classical lattice models describing first-order phase transitions, and study the finite-size scaling of the magnetization and susceptibility. In order to model the effects of an actual surface in systems such as small magnetic clusters, we consider models with free boundary conditions. For a field-driven transition with two coexisting phases at the infinite-volume transition pointh=h _t , we prove that the low-temperature, finite-volume magnetizationm _free(L, h) per site in a cubic volume of sizeL ^d behaves like $$m_{free} (L,h) = \frac{{m_ + + m_ - }}{2} + \frac{{m_ + - m_ - }}{2}tanh\left[ {\frac{{m_ + - m_ - }}{2}L^d (h - h_\chi (L))} \right] + O\left( {\frac{1}{L}} \right)$$ whereh _x (L) is the position of the maximum of the (finite-volume) susceptibility andm _± are the infinite-volume magnetizations ath=h _t +0 andh=h _t ?0, respectively. We show thath _x (L) is shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t provided the surface free energies of the two phases at the transition point are different. This should be compared with the shift for periodic boundary conditions, which for an asymmetric transition with two coexisting phases is proportional only to 1/L ^2d . One can consider also other definitions of finite-volume transition points, for example, the positionh _U (L) of the maximum of the so-called Binder cumulantU _free(L,h). Whileh _U (L) is again shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t , its shift with respect toh _χ (L) is of the much smaller order 1/L ^2d . We give explicit formulas for the proportionality factors, and show that, in the leading 1/L ^2d term, the relative shift is the same as that for periodic boundary conditions.