arXiv subjects

X. S. Chen

Publications and source records attributed to X. S. Chen.

33 records · Page 2Linked to original sources

arXiv2004

Nonuniversal finite-size scaling in anisotropic systems

We study the bulk and finite-size critical behavior of the O$(n)$ symmetric $ϕ^4$ theory with spatially anisotropic interactions of non-cubic symmetry in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class, two-scale factor universality is absent in bulk correlation functions, and finite-size scaling functions including the Privman-Fisher scaling form of the free energy, the Binder cumulant ratio and the Casimir amplitude are shown to be nonuniversal. In particular it is shown that, for anisotropic confined systems, isotropy cannot be restored by an anisotropic scale transformation.

cond-mat.stat-mech↗

arXiv2002

Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions

We calculate finite-size effects of the Gaussian model in a L\times \tilde L^{d-1} box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2 3 but logarithmic deviations from finite-size scaling are found for the free energy and energy density at the Gaussian upper borderline dimension d* =3. The logarithms are related to the vanishing critical exponent 1-α-ν=(d-3)/2 of the Gaussian surface energy density. The latter has a cusp-like singularity in d>3 dimensions. We show that these properties are the origin of nonscaling finite-size effects in the mean spherical model with free boundary conditions in d>=3 dimensions. At bulk T_c in d=3 dimensions we find an unexpected non-logarithmic violation of finite-size scaling for the susceptibility χ\sim L^3 of the mean spherical model in film geometry whereas only a logarithmic deviation χ\sim L^2 \ln L exists for box geometry. The result for film geometry is explained by the existence of the lower borderline dimension d_l = 3, as implied by the Mermin-Wagner theorem, that coincides with the Gaussian upper borderline dimension d*=3. For 3 =T_c.

cond-mat↗

arXiv2002

Non-universal critical Casimir force in confined $^4$He near the superfluid transition

We present the results of a one-loop calculation of the effect of a van der Waals type interaction potential $\sim | {\bf x} |^{-d-σ}$ on the critical Casimir force and specific heat of confined $^4$He near the superfluid transition. We consider a $^4$He film of thickness $L$. In the region $L \gtrsim ξ$ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of $O (ξ^2 L^{-d-σ})$ to the critical temperature dependence of the Casimir force above $T_λ$ that dominates the universal scaling contribution $\sim e^{- L/ξ}$ predicted by earlier theories. For the specific heat we find subleading non-scaling contributions of $O(L^{-1})$ and $O(L^{-d-σ})$.

cond-mat.stat-mech↗

arXiv2001

Violation of finite-size scaling for the free energy near criticality

The singular part of the finite-size free energy density $f_s$ of the O($n$) symmetric $ϕ^4$ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of $f_s$ near $T_c$. For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above $T_c$ for both periodic and Dirichlet boundary conditions.

cond-mat.stat-mech↗

arXiv2001

Non-universal size dependence of the free energy of confined systems near criticality

The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric $ϕ^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $Λ$ causes a non-universal leading size dependence $f_s \sim Λ^{d-2} L^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.

cond-mat.stat-mech↗

arXiv2000

Strange quark polarization of the nucleon: A parameter-independent prediction of the chiral potential model

We perform a one-loop calculation of the strange quark polarization ($Δs$) of the nucleon in a SU(3) chiral potential model. We find that if the intermediate excited quark states are summed over in a proper way, i.e., summed up to a given energy instead of given radial and orbital quantum numbers, $Δs$ turns out to be almost independent of {\em all} the model parameters: quark masses, scalar- and vector-potential strengths. The contribution from the quark-antiquark pair creation and annihilation ``$Z$'' diagrams is found to be significant. Our numerical results agree quite reasonably with experiments and lattice QCD calculations.

hep-ph↗

arXiv2000

Positive strangeness contribution to the nucleon magnetic moment in a relativistic chiral potential model

The strangeness contribution to the nucleon magnetic moment is calculated at the one-loop level in a relativistic SU(3) chiral potential model and is found to be {\em positive}, that is, with an {\em opposite} sign to the nucleon strangeness polarization. It is the ``Z'' diagram that violates the usual relation between spin and magnetic moment. The positive value is due to the contribution from the intermediate excited quark states, while the intermediate ground state gives a negative contribution. Our numerical results agree quite well with the new measurement of the SAMPLE Collaboration.

hep-ph↗

arXiv2000

Renormalization of quark axial current in the chiral potential model

Non-conserved composite operators like the quark axial current have divergent matrix elements therefore must be renormalized. We explore how this can be done in quark model calculations where the systematic procedure of dimensional regularization and minimal subtraction is not applicable. We propose a most natural and convenient regularization scheme of cutting the intermediate quark states over which we sum in loop diagram calculations at a certain energy. We show that this scheme works perfectly for the quark axial current and we obtain the quark spin contribution to the proton spin: $Δ_u=0.82$, $Δ_d=-0.43$, $Δ_s=-0.10$, which is in excellent agreement with experiments.

hep-ph↗

arXiv2000

Universality and nonmonotonic finite-size effects above the upper critical dimension

We analyze universal and nonuniversal finite-size effects of lattice systems in a $L^d$ geometry above the upper critical dimension d = 4 within the O(n) symmetric $ϕ^4$ lattice theory. On the basis of exact results for $n \to\infty$ and one-loop results for n = 1 we identify significant lattice effects that cannot be explained by the $ϕ^4$ continuum theory. Our analysis resolves longstanding discrepancies between earlier asymptotic theories and Monte Carlo (MC) data for the five-dimensional Ising model of small size. We predict a {\it nonmonotonic} L dependence of the scaled susceptibility $χL^{-d/2}$ at $T_c$ with a weak maximum that has not yet been detected by MC data.

cond-mat.stat-mech↗

arXiv1999

Relation between bulk order-parameter correlation function and finite-size scaling

We study the large-$r$ behavior of the bulk order-parameter correlation function $G(\bf{r})$ for $T>T_c$ within the lattice $ϕ^4$ theory. We also study the large-$L$ behavior of the susceptibility $χ$ of the confined lattice system of size $L$ with periodic boundary conditions. The large-$L$ behavior of $χ$ is closely related to the large-$r$ behavior of $G(\bf{r})$. Explicit results are derived for $d>2$. Finite-size scaling must be formulated in terms of the anisotropic exponential correlation length $ξ_1$ that governs the decay of $G(\bf{r})$ for large $r$ rather than in terms of the isotropic correlation length $ξ$ defined via the second moment of $G(\bf{r})$. This result modifies a recent interpretation concerning an apparent violation of finite-size scaling in terms of $ξ\neq ξ_1$. Exact results for the $d=1$ Ising model illustrate our conclusions. Furthermore, we show that the exponential finite-size behavior for $L/ξ\gg 1$ is not captured by the standard perturbation approach that separates the lowest mode from the higher modes. Consequences for the theory of finite-size effects for $d>4$ are discussed. The two-variable finite-size scaling form predicts an approach $\propto e^{-L/ξ_1}$ to the bulk critical behavior whereas a single-variable scaling form implies a power-law approach $\propto L^{-d}$.

cond-mat.stat-mech↗

arXiv1999

Nonmonotonic External Field Dependence of the Magnetization in a Finite Ising Model: Theory and MC Simulation

Using $ϕ^4$ field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization $M$ for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state $h/M^δ= f(hL^{βδ/ν}, t/h^{1/βδ})$ where $t=(T-T_c)/T_c$ is the reduced temperature, $h$ is the external field and $L$ is the size of system. Below $T_c$ and at $T_c$ the theory predicts a nonmonotonic dependence of $f(x,y)$ with respect to $x \equiv hL^{βδ/ν}$ at fixed $y \equiv t/h^{1/βδ}$ and a crossover from nonmonotonic to monotonic behaviour when $y$ is further increased. These results are confirmed by MC simulation. The scaling function $f(x,y)$ obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value $f(\infty,0)$ at $T_c$.

cond-mat.stat-mech↗

arXiv1999

Cutoff and lattice effects in the $\varphy^4$ theory of confined systems

We study cutoff and lattice effects in the O(n) symmetric $ϕ^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $ϕ^4$ field theory at finite cutoff $Λ$ predicts the nonuniversal deviation $\sim (ΛL)^{-2}$ from asymptotic bulk critical behavior that violates finite-size scaling and disagrees with the deviation $\sim e^{-cL}$ that we find in the $ϕ^4$ lattice model. The exponential size dependence requires a non-perturbative treatment of the $ϕ^4$ model. Our arguments indicate that these results should be valid for general $n$ and $d > 2$.

cond-mat.stat-mech↗

arXiv1999

Violation of Finite-Size Scaling in Three Dimensions

We reexamine the range of validity of finite-size scaling in the $ϕ^4$ lattice model and the $ϕ^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $ϕ^4$ theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size $L$ with periodic boundary conditions we analyze the approach towards bulk critical behavior as $L \to \infty$ at fixed $ξ$ for $T > T_c$ where $ξ$ is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the $ϕ^4$ lattice model and the $ϕ^4$ field theory in the region $L \gg ξ$. The non-scaling effects in the field theory and in the lattice model differ significantly from each other.

cond-mat.stat-mech↗

arXiv1998

Lattice $ϕ^4$ theory of finite-size effects above the upper critical dimension

We present a perturbative calculation of finite-size effects near $T_c$ of the $ϕ^4$ lattice model in a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions for $d > 4$. The structural differences between the $ϕ^4$ lattice theory and the $ϕ^4$ field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters.One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite $ξ/L$ where $ξ$ is the bulk correlation length. At $T_c$, the large-$L$ behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to $T_c$ of the lattice model, such as $T_{max}(L)$ of the maximum of the susceptibility $χ$, are found to scale asymptotically as $T_c - T_{max}(L) \sim L^{-d/2}$, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict $χ_{max} \sim L^{d/2}$ asymptotically. On a quantitative level, the asymptotic amplitudes of this large -$L$ behavior close to $T_c$ have not been observed in previous MC simulations at $d = 5$ because of nonnegligible finite-size terms $\sim L^{(4-d)/2}$ caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the $L^{(4-d)/2}$ and $L^{4-d}$ terms predicted by our theory.

cond-mat.stat-mech↗

arXiv1997

Finite-Size Effects in the $ϕ^{4}$ Field Theory Above the Upper Critical Dimension

We demonstrate that the standard O(n) symmetric $ϕ^{4}$ field theory does not correctly describe the leading finite-size effects near the critical point of spin systems on a $d$-dimensional lattice with $d > 4$. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For $n \to \infty$ and $n=1$ explicit results are given for the susceptibility and for the Binder cumulant. They imply that recent analyses of Monte-Carlo results for the five-dimensional Ising model are not conclusive.

cond-mat↗