arXiv subjects

P. Jakubczyk

Publications and source records attributed to P. Jakubczyk.

12 recordsLinked to original sources

arXiv2016

Repulsive Casimir forces at quantum criticality

We study the Casimir effect in the vicinity of a quantum critical point. As a prototypical system we analyze the $d$-dimensional imperfect (mean-field) Bose gas enclosed in a slab of extension $L^{d-1}\times D$ and subject to periodic boundary conditions. The thermodynamic state is adjusted so that $L\ggλ\gg D\ggł_{mic}$, where $λ\sim T^{-1/2}$ is the thermal de Broglie length, and $l_{mic}$ denotes microscopic lengthscales. Our exact analysis indicates that the Casimir force in the above specified regime is generically repulsive and decays either algebraically or exponentially, with a non-universal amplitude.

cond-mat.stat-mech↗

arXiv2014

Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

We reexamine the two-dimensional linear O(2) model ($φ^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension $η(\Tkt)\simeq 0.24$ and the stiffness jump $ρ_s(\Tkt^-)\simeq 0.64$ at the transition temperature $\Tkt$, in very good agreement with the exact results $η(\Tkt)=1/4$ and $ρ_s(\Tkt^-)=2/π$, as well as an essential singularity of the correlation length in the high-temperature phase as $T\to \Tkt$.

cond-mat.stat-mech↗

arXiv2013

Quantum criticality of the imperfect Bose gas in d dimensions

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 ξdevelops 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.

cond-mat.stat-mech↗

arXiv2013

The imperfect Bose gas in d dimensions: critical behavior and Casimir forces

We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exponentially as a function of D with the bulk correlation length determining the relevant length scale. For T=T_c and for T 4 and T\leq T_c.

cond-mat.stat-mech↗

arXiv2011

Capillary-wave models and the effective average action scheme of functional renormalization group

We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension d\geq 2. Exploiting the non-uniqueness of the renormalization-group cutoff scheme, we find however, that the capillary parameter omega is a scheme-dependent quantity below d=3. For d=3 the parameter omega is perfectly robust against scheme variation.

cond-mat.stat-mech↗

arXiv2011

Critical temperature and Ginzburg region near a quantum critical point in two-dimensional metals

We compute the transition temperature $T_c$ and the Ginzburg temperature $T_{\rm G}$ above $T_c$ near a quantum critical point at the boundary of an ordered phase with a broken discrete symmetry in a two-dimensional metallic electron system. Our calculation is based on a renormalization group analysis of the Hertz action with a scalar order parameter. We provide analytic expressions for $T_c$ and $T_{\rm G}$ as a function of the non-thermal control parameter for the quantum phase transition, including logarithmic corrections. The Ginzburg regime between $T_c$ and $T_{\rm G}$ occupies a sizable part of the phase diagram.

cond-mat.str-el↗

arXiv2010

Finite temperature crossovers near quantum tricritical points in metals

We present a renormalization group treatment of quantum tricriticality in metals. Applying a set of flow equations derived within the functional renormalization group framework we evaluate the correlation length in the quantum critical region of the phase diagram, extending into finite temperatures above the quantum critical or tricritical point. We calculate the finite temperature phase boundaries and analyze the crossover behavior when the system is tuned between quantum criticality and quantum tricriticality.

cond-mat.str-el↗

arXiv2010

Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability

We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a d-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge.

cond-mat.str-el↗

arXiv2009

Phase boundary and finite temperature crossovers of the quantum Ising model in two dimensions

We revisit the two-dimensional quantum Ising model by computing renormalization group flows close to its quantum critical point. The low but finite temperature regime in the vicinity of the quantum critical point is squashed between two distinct non-Gaussian fixed points: the classical fixed point dominated by thermal fluctuations and the quantum critical fixed point dominated by zero-point quantum fluctuations. Truncating an exact flow equation for the effective action we derive a set of renormalization group equations and analyze how the interplay of quantum and thermal fluctuations, both non-Gaussian in nature, influences the shape of the phase boundary and the region in the phase diagram where critical fluctuations occur. The solution of the flow equations makes this interplay transparent: we detect finite temperature crossovers by computing critical exponents and we confirm that the power law describing the finite temperature phase boundary as a function of control parameter is given by the correlation length exponent at zero temperature as predicted in an epsilon-expansion with epsilon=1 by Sachdev, Phys. Rev. B 55, 142 (1997).

cond-mat.stat-mech↗

arXiv2009

Renormalized phi^6 model for quantum phase transitions in systems of itinerant fermions

We study the impact of quantum and thermal fluctuations on properties of quantum phase transitions occurring in systems of itinerant fermions with main focus on the order of these transitions. Our approach is based on a set of flow equations derived within the functional renormalization group framework, in which the order parameter is retained as the only degree of freedom, and where the effective potential is parametrized with a phi^6 form allowing for both first and second order scenarios. We find a tendency to turn the first order transitions within the bare model into second order transitions upon accounting for the order parameter fluctuations. We compute the first and second order phase boundary lines T_c as a function of a non-thermal control parameter a_2 in the vicinity of a quantum phase transition. We analyze crossovers of the shift exponent psi governing the shape of the T_c line when the system is tuned close to a quantum tricritical scenario, where a second order phase transition line terminates at a quantum tricritical point.

cond-mat.str-el↗

arXiv2008

Renormalization group for phases with broken discrete symmetry near quantum critical points

We extend the Hertz-Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. Using a set of coupled flow equations derived within the functional renormalization group framework, we compute the second order phase transition line T_c(delta), with delta a non-thermal control parameter, near a quantum critical point. We analyze the interplay and relative importance of quantum and classical fluctuations at different energy scales, and we compare the Ginzburg temperature T_G to the transition temperature T_c, the latter being associated with a non-Gaussian fixed-point.

cond-mat.str-el↗

arXiv2006

Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width $2L$ placed on an otherwise homogeneous, planar, solid surface. The excess point free energy $η(L,T)$ associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way $η(L,T)$ varies with $L$ depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of $L$ in the limit $L\to\infty$ for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case $η(L,T)$ converges for large $L$ to $2η_0$, where $η_0$ is the corresponding point tension, and the dominant $L$-dependent correction to $2η_0$ decays exponentially. The interaction between the liquid layer inhomogeneities at $-L$ and $L$ for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.

cond-mat.stat-mech↗