Latest Papers in Condensed Matter Physics
Statistical Mechanics
Yamen Hamdouni
2019-02-11
We investigate analytically the magnetization of Heisenberg ferromagnetic lattices in one and two dimensions, and we derive approximate expressions that are valid at high and low temperatures. In the case of the spin-
Heisenberg XX chain in a transverse field, we show that, when the applied magnetic field 
exceeds its critical value 
, where 
is the exchange coupling constant, the magnetization per site deviates at low temperatures from its saturation value, , following a power series with terms involving the power laws 
, 
, 
..etc. When 
, the zero temperature magnetization per spin turns out to be equal to 
. In this case, the temperature dependence of the magnetization is given by a series expansion with power laws of the form 
, 
, 
,...etc. In both cases, the coefficients of the expansions are temperature-dependent and are explicitly derived. Using he properties of the Eulerian polynomials, we show that, because of the fast convergence of the derived series for the Fermi-Dirac and the Bose-Einstein distributions, it is possible (in particular in strong magnetic fields) to express the magnetization of the Heisenberg model in a simple analytical form. Furthermore, the analytical results are compared with the exact numerical ones.
Nathaniel Rupprecht, Dervis Vural
2019-03-13
Nearly all theoretical analyses of the Maxwell's demon focuses on its energetic and entropic costs of operation. Here, we focus on its rate of operation. In our model, a demon's rate limitation stems from its finite response time and gate area. We determine the rate limits of mass and energy transfer, as well as entropic reduction for four such demons: Those that select particles according to (1) direction, (2) energy, (3) number and (4) entropy. In addition to rate limitations we also calculate their coefficients of performance and compare it with that of an ideal demon. Lastly, we determine the optimal gate size for a demon with finite response time.
Martin Buchacek, Vadim B. Geshkenbein, Roland Willa, Gianni Blatter
2019-03-21
We study thermal effects on pinning and creep in type-II superconductors where vortices interact with a low density 
of strong point-like defects with pinning energy 
and extension 
, the vortex core size. Defects are classified as strong if the interaction between a single pin and an individual vortex leads to the appearance of bistable solutions describing pinned and free vortex configurations. Extending the strong pinning theory to account for thermal fluctuations, we provide a quantitative analysis of vortex depinning and creep. We determine the thermally activated transitions between bistable states using Kramer's rate theory and find the non-equilibrium steady-state occupation of vortex states. The latter depends on the temperature and vortex velocity 
and determines the current--voltage (or force--velocity) characteristic of the superconductor at finite temperatures. We find that the 
linear excess-current characteristic 
with its sharp transition at the critical current density 
, keeps its overall shape but is modified in three ways due to thermal creep: a downward renormalization of to the thermal depinning current density 
, a smooth rounding of the characteristic around 
, and the appearance of thermally assisted flux flow (TAFF) 
at small drive 
, with the activation barrier 
defined through the energy landscape at the intersection of free and pinned branches. This characteristic emphasizes the persistence of pinning of creep at current densities beyond critical.
S. Redner
2018-11-29
This mini-review presents extensions of the voter model that incorporate various plausible features of real decision-making processes by individuals. Although these generalizations are not calibrated by empirical data, the resulting dynamics are suggestive of realistic collective social behaviors.
Kay Joerg Wiese, Andrei A. Fedorenko
2018-02-24
Self-avoiding walks (SAWs) and loop-erased random walks (LERWs) are two ensembles of random paths with numerous applications in mathematics, statistical physics and quantum field theory. While SAWs are described by the 
limit of 
-theory with 
-symmetry, LERWs have no obvious field-theoretic description. We analyse two candidates for a field theory of LERWs, and discover a connection between the corresponding and a priori unrelated theories. The first such candidate is the -symmetric theory at 
whose link to LERWs was known in two dimensions due to conformal field theory. Here it is established in arbitrary dimension via a perturbation expansion in the coupling constant. The second candidate is a field theory for charge-density waves pinned by quenched disorder, whose relation to LERWs had been conjectured earlier using analogies with Abelian sandpiles. We explicitly show that both theories yield identical results to 4-loop order and give both a perturbative and a non-perturbative proof of their equivalence. This allows us to compute the fractal dimension of LERWs to order 
where 
. In particular, in 
our theory gives 
, in excellent agreement with the estimate 
of numerical simulations.
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