arXiv subjects

Angsula Ghosh

Publications and source records attributed to Angsula Ghosh.

14 recordsLinked to original sources

arXiv2008

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 $Δ$ (such that $Δ=0$ and $Δ=1$ 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.

cond-mat.stat-mech↗

arXiv2005

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.

cond-mat.str-el↗

arXiv2001

Tricritical behaviour in deterministic aperiodic Ising systems

We use a mixed-spin model, with aperiodic ferromagnetic exchange interactions and crystalline fields, to investigate the effects of deterministic geometric fluctuations on first-order transitions and tricritical phenomena. The interactions and the crystal field parameters are distributed according to some two-letter substitution rules. From a Migdal-Kadanoff real-space renormalization-group calculation, which turns out to be exact on a suitable hierarchical lattice, we show that the effects of aperiodicity are qualitatively similar for tricritical and simple critical behaviour. In particular, the fixed point associated with tricritical behaviour becomes fully unstable beyond a certain threshold dimension (which depends on the aperiodicity), and is replaced by a two-cycle that controls a weakened and temperature-depressed tricritical singularity.

cond-mat.stat-mech↗

arXiv2001

Mixing of $d_{x^2-y^2}$ and $d_{xy}$ superconducting states for different filling and temperature

We investigate the solution of the gap equation for mixed order parameter symmetry states as a function of filling using a two-dimensional tight-binding model incorporating second-neighbor hopping for tetragonal and orthorhombic lattice. The principal (major) component of the order parameter is taken to be of the $d_{x^2-y^2}$ type. As suggested in several investigations the minor component of the order parameter is taken to be of the $d_{xy}$ type. Both the permissible mixing angles 0 and $π/2$ between the two components are considered. As a function of filling pronounced maxima of $d_{x^2-y^2}$ order parameter is accompanied by minima of the $d_{xy}$ order parameter. At fixed filling, the temperature dependence of the two components of the order parameter is also studied in all cases. The variation of critical temperature $T_c$ with filling is also studied and $T_c$ is found to increase with second-neighbor hopping.

cond-mat.str-el↗

arXiv2000

Mixing of superconducting $d_{x^2-y^2}$ 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 $π/2$. 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.

cond-mat.supr-con↗

arXiv2000

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.

cond-mat.stat-mech↗

arXiv1999

Two phase transitions in ${(d_{x^2-y^2}+is)}$-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.

cond-mat.supr-con↗

arXiv1999

Phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $ d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $ d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.

cond-mat.supr-con↗

arXiv1999

Phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+id_{xy}$ superconductor

The temperature dependencies of specific heat and spin susceptibility of a coupled $d_{x^2-y^2} +id_{xy}$ superconductor in the presence of a weak $d_{xy}$ component are investigated in the tight-binding model (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature $T_c$, first a less ordered $d_{x^2-y^2}$ superconductor is created, which changes to a more ordered $d_{x^2-y^2} +id_{xy}$ superconductor at $T_{c1} (<T_c)$. This manifests in two second order phase transitions 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.

cond-mat.supr-con↗

arXiv1998

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

nucl-th↗

arXiv1998

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.

cond-mat.str-el↗

arXiv1997

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 $ξ$ 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 $ξ$ 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.

cond-mat.supr-con↗

arXiv1997

Universal scaling in BCS superconductivity in three dimensions in non-$s$ 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 $ξ$ and a large critical temperature, $T_c$, appropriate for some high-$T_c$ materials. The BCS gap, $T_c$, $ξ$ 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.

cond-mat.supr-con↗

arXiv1997

Renormalization in Nonrelativistic Quantum Mechanics

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behavior and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.

hep-th↗