Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L–d, the same as for periodic boundary conditions, the shift is much larger, of order L–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust. 相似文献
The influence of 200 keV Ar-ion irradiation on the interlayer coupling in the Fe/Cr multilayer system exhibiting the giant magnetoresistance effect (GMR) is studied by conversion electron Mössbauer spectroscopy (CEMS), VSM hysteresis loops, magnetoresistivity and electric resistivity measurements and supplemented by the small-angle X-ray diffraction (SAXRD). The increase of Ar ion dose causes an increase of interface roughness, as evidenced by the increase of the Fe step-sites detected by CEMS as a result of which the GMR gradually decreases and vanishes at doses exceeding 1×1014 Ar/cm2. A degradation of GMR with increasing Ar-ion dose is related to the formation of pinholes between Fe layers and the decrease of the antiferromagnetically coupled fraction.
We discuss the simple, randomly driven systemdx/dt = –x –x3 +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number ()1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp2/2 +m2x2/2 +vx4 +x6/2, we evaluate the path integral on a lattice by assuming that thex6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy. 相似文献
The fabrication of flexible surface-enhanced Raman scattering (SERS) substrates for sensitive detection on uneven or irregular surfaces is challenging. In this study, a flexible dual plasmonic SERS (FDPS) substrate rationally constructed using Au nanoparticle (AuNP) arrays/aligned Ag nanowires (AgNWs) and elastic polyurethane (PU) is demonstrated. It exhibits high sensitivity (detection limit of 10−8 m for melamine and 10−10 m for malachite green) and excellent reproducibility. The well-designed structure of AuNP arrays/aligned AgNWs fabricated using block copolymer self-assembly and oil–water–air interfacial self-assembly successfully enhances the electromagnetic field through plasmonic coupling. In addition, the FDPS substrate retains a high SERS sensitivity after exposure to air at room temperature for 30 days because of the high stability of AuNP arrays and antioxidation characteristic of the PU covered on the aligned AgNWs. Even after undergoing stretching, bending, and twisting for 100 cycles, the FDPS substrate maintains a stable SERS activity owing to the introduction of the elastic PU. This study demonstrates a potential application of SERS detection under practical conditions for irregular surfaces and may be helpful in the development of flexible sensors. 相似文献