Renormalization-group analysis of the dilute Bose system in<i>d</i>dimensions at finite temperature

Crişan, M.; Bodea, D.; Grosu, I.; Ţifrea, I.

doi:10.1088/0305-4470/35/2/305

Cited by 17 publications

(17 citation statements)

References 43 publications

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“…In this case the dynamical critical exponent value is z = 2, and the renormalization group equations (3)-(5) are similar to those of the weakly interacting Bose gas 25,26 . Equation (3) has a trivial solution of the form…”

Section: B U(1)symmetrymentioning

confidence: 74%

Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

et al. 2005

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We use the Renormalization Group method to study the magnetic field influence on the BoseEinstein condensation of interacting dilute magnons in three dimensional spin systems. We first considered a model with SU (2) symmetry (universality class z = 1) and we obtain for the critical magnetic field a power law dependence on the critical temperature, [Hc(T ) − Hc(0)] ∼ T 2 . In the case of U (1) symmetry (universality class z = 2) the dependence is different, and the magnetic critical field depends linearly on the critical temperature, [Hc(T ) − Hc(0)] ∼ T . By considering a more relevant model, which includes also the system's anisotropy, we obtain for the same symmetry class a T 3/2 dependence of the magnetic critical field on the critical temperature. We discuss these theoretical predictions of the renormalization group in connection with experimental results reported in the literature.

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Section: B U(1)symmetrymentioning

confidence: 74%

Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

et al. 2005

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“…A basic aspect of Bose-Einstein condensation is the actual order of the transition. In the non-interacting case it is third order (within the Ehrenfest classification), On the other hand, order-parameter based studies of dilute Bose systems [8,9,10,11,12,13,14,15,16] as well as related effective low-energy bosonic models for underlying Fermi systems [6,17,18,19] typically truncate the effective action at quartic order biasing the system towards a second-order transition. It is however well known that different fluctuation-related effects tend to change the order of both thermal and quantum phase transitions [5,20,21,22,23,24,25,26,27,28], and often destabilize them towards first-order.…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality of the imperfect Bose gas inddimensions

Jakubczyk¹,

Napiórkowski²

2013

J. Stat. Mech.

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Abstract. We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose-Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d > 2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum critical point focusing on the behavior of the correlation length ξ. The length ξ develops an essential singularity exclusively for d = 2. We follow the evolution of the phase diagram varying d. For d > 2 our results agree with renormalization-group based analysis of the effective bosonic order-parameter models with the dynamical exponent z = 2.

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“…Along this direction, a rich low-temperature scenario was obtained in Refs. [4][5][6] for the case of an interacting Bose gas with the chemical potential fixed at its QCP value.…”

Section: Introductionmentioning

confidence: 99%

Low-temperature quantum critical behaviour of systems with transverse Ising-like intrinsic dynamics

D'Auria

Cesare

Rabuffo

2003

Physica A: Statistical Mechanics and its Applications

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The low-temperature properties and crossover phenomena of d-dimensional transverse Ising-like systems within the influence domain of the quantum critical point are investigated solving the appropriate one-loop renormalization group equations. The phase diagram is obtained near and at d = 3 and several sets of critical exponents are determined which describe different responses of a system to quantum fluctuations according to the way of approaching the quantum critical point. The results are in remarkable agreement with experiments for a wide variety of compounds exhibiting a quantum phase transition, as the ferroelectric oxides and other displacive systems.1

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Renormalization-group analysis of the dilute Bose system inddimensions at finite temperature

Cited by 17 publications

References 43 publications

Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

Quantum criticality of the imperfect Bose gas inddimensions

Low-temperature quantum critical behaviour of systems with transverse Ising-like intrinsic dynamics

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