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Register a new userMetastable Reverse-Phase Droplets within Ordered Phases: Renormalization-Group Calculation of Field and Temperature Dependence of Limiting Size
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Metastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase and noting whether the reverse-phase magnetization sustains. The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of field and temperature for the Ising model in three dimensions. The method also yields hysteresis loops for finite systems, as function of temperature and system size.
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The existence and limits of metastable droplets have been calculated using finite-system renormalization-group theory, for q-state Potts models in spatial dimension d=3. The dependence of the droplet critical sizes on magnetic field, temperature, and number of Potts states q has been calculated. The same method has also been used for the calculation of hysteresis loops across first-order phase transitions in these systems. The hysteresis loop sizes and shapes have been deduced as a function of magnetic field, temperature, and number of Potts states q. The uneven appearance of asymmetry in the hysteresis loop branches has been noted. The method can be extended to criticality and phase transitions in metastable phases, such as in surface-adsorbed systems and water.
It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $gto 0$.
A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher-order tensor renormalization group is proposed. The physical observables are represented by impurity tensors. A systematic summation scheme provides coarse-grained tensors including multiple impurities. Our method is compared with the Monte Carlo method on the two-dimensional Potts model. While the nature of the transition of the $q$-state Potts model has been known for a long time owing to the analytical arguments, a clear numerical confirmation has been difficult due to extremely long correlation length in the weakly first-order transitions, e.g., for $q=5$. A jump of the Binder ratio precisely determines the transition temperature. The finite-size scaling analysis provides critical exponents and distinguishes the weakly first-order and the continuous transitions.
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow equations obtained within this scheme, and compute the two-point functions of the O(N) theories at criticality, in two and three dimensions. Excellent results are obtained for both universal and non-universal quantities at modest numerical cost.
A quantum tricritical point is shown to exists in coupled time-reversal symmetry (TRS) broken Majorana chains. The tricriticality separates topologically ordered, symmetry protected topological (SPT), and trivial phases of the system. Here we demonstrate that the breaking of the TRS manifests itself in an emergence of a new dimensionless scale, $g = alpha(xi) B sqrt{N}$, where $N$ is the system size, $B$ is a generic TRS breaking field, and $alpha(xi)$, with $alpha(0)equiv 1$, is a model-dependent function of the localization length, $xi$, of boundary Majorana zero modes at the tricriticality. This scale determines the scaling of the finite size corrections around the tricriticality, which are shown to be {it universal}, and independent of the nature of the breaking of the TRS. We show that the single variable scaling function, $f(w)$, $wpropto m N$, where $m$ is the excitation gap, that defines finite-size corrections to the ground state energy of the system around topological phase transition at $B=0$, becomes double-scaling, $f=f(w,g)$, at finite $B$. We realize TRS breaking through three different methods with completely different lattice details and find the same universal behavior of $f(w,g)$. In the critical regime, $m=0$, the function $f(0,g)$ is nonmonotonic, and reproduces the Ising conformal field theory scaling only in limits $g=0$ and $grightarrow infty$. The obtained result sets a scale of $N gg 1/(alpha B)^2$ for the system to reach the thermodynamic limit in the presence of the TRS breaking. We derive the effective low-energy theory describing the tricriticality and analytically find the asymptotic behavior of the finite-size scaling function. Our results show that the boundary entropy around the tricriticality is also a universal function of $g$ at $m=0$.
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