Two phase transitions in (dx2−y2+is){(d_{x^2-y^2}+is)}-wave superconductors

We study numerically the temperature dependencies of specific heat, susceptibility, penetration depth, and thermal conductivity of a coupled $(d_{x^2-y^2}+is)$-wave Bardeen-Cooper-Schreiffer superconductor in the presence of a weak s-wave component (1) on square lattice and (2) on a lattice with orthorhombic distorsion. As the temperature is lowered past the critical temperature $T_c$, a less ordered superconducting phase is created in $d_{x^2-y^2}$ wave, which changes to a more ordered phase in $(d_{x^2-y^2}+is)$ wave at $T_{c1}$. This manifests in two second-order phase transitions. The two phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of the superconducting observables exhibit a change from power-law to exponential behavior as temperature is lowered below $T_{c1}$ and confirm the new phase transition.Comment: Latex file, 6 pages, 7 postscript figures, Accepted in Physica

Universal scaling in BCS superconductivity in three dimensions in non-ss waves

The solutions of a renormalized BCS equation are studied in three space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length $\xi$ and a large critical temperature, $T_c$, appropriate for some high-$T_c$ materials. The BCS gap, $T_c$, $\xi$ and specific heat $C_s(T_c)$ as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below $T_c$ in $p$ and $d$ waves.Comment: 9 pages of LATEX and 5 post-script figures. Accepted in European Physical Journal

Mixing of superconducting dx2−y2d_{x^2-y^2} state with s-wave states for different filling and temperature

We study the order parameter for mixed-symmetry states involving a major $d_{x^2-y^2}$ state and various minor s-wave states ($s$, $s_{xy}$, and $s_{x^2+y^2}$) for different filling and temperature for mixing angles 0 and $\pi/2$. We employ a two-dimensional tight-binding model incorporating second-neighbor hopping for tetragonal and orthorhombic lattice. There is mixing for the symmetric $s$ state both on tetragonal and orthorhombic lattice. The $s_{xy}$ state mixes with the $d_{x^2-y^2}$ state only on orthorhombic lattice. The $s_{x^2+y^2}$ state never mixes with the $d_{x^2-y^2}$ state. The temperature dependence of the order parameters is also studied.Comment: 10 pages, 9 figures, accepted in Physica

Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: a renormalization-group approach

Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter $\Delta$ (such that $\Delta=0$ and $\Delta=1$ correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the \textit{classical} isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.Comment: 6 pages, 3 figures, to be published in Phys. Rev.

Field behavior of an Ising model with aperiodic interactions

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal-Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.Comment: 9 pages, 1 figure (included). Accepted for publication in Int. J. Mod. Phys.

Universal scaling in BCS superconductivity in two dimensions in non-s waves

The solutions of a renormalized BCS model are studied in two space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials. The gap parameter, the critical temperature $T_c$, the coherence length $\xi$ and the jump in specific heat at $T_c$ as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small $\xi$ and large $T_c$ appropriate to those for high-$T_c$ cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in $p$ and $d$ waves.Comment: 11 pages, LATEX, 4 postscript figures embedded using eps

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behavior in temperature dependencies of some observables in $(s+id)$-wave BCS superconductivity in the presence of a weak $s$ wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature $T_c$, a less ordered superconducting phase is created in $d$ wave, which changes to a more ordered phase in $(s+id)$ wave at $T_{c1}$ ($< T_c$). The presence of two phase transitions manifest in two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of susceptibility, penetration depth, and thermal conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures

Non-uniform phases in metals with local moments

The two-dimensional Kondo lattice model with both nearest and next-nearest neighbor exchange interactions is studied within a mean-field approach and its phase diagram is determined. In particular, we allow for lattice translation symmetry breaking. We observe that the usual uniform inter-site order parameter is never realized, being unstable towards other more complex types of order. When the nearest neighbor exchange J_1 is ferromagnetic the flux phase is always the most stable state, irrespective of the value of the next-nearest-neighbor interaction J_2. For antiferromagnetic J_1, however, either a columnar or a flux phase is realized, depending on conduction electron filling and the value of J_2.Comment: 5 pages, 7 figure