arXiv subjects

Hirofumi Yamada

Publications and source records attributed to Hirofumi Yamada.

At least 19 recordsLinked to original sources

arXiv2016

Generalized binomial transform applied to the divergent series

The divergent series for a function defined through Lapalce integral and the ground state energy of the quartic anharmonic oscillator to large orders are studied to test the generalized binomial transform which is the renamed version of $δ$-expansion proposed recently. We show that, by the use of the generalized binomial transform, the values of functions in the limit of zero of an argument is approximately computable from the series expansion around the infinity of the same argument. In the Laplace integral, we investigate the subject in detail with the aid of Mellin transform. In the anharmonic oscillator, we compute the strong coupling limit of the ground state energy and also the expansion coefficients at strong coupling from the weak coupling perturbation series. The obtained result is compared with that of the linear delta expansion.

quant-ph↗

arXiv2016

Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy

We demonstrated visualization of Au nanoparticles buried 300 nm into a polymer matrix by measurement of the thermal noise spectrum of a microcantilever with a tip in contact to the polymer surface. The subsurface Au nanoparticles were detected as the variation in the contact stiffness and damping reflecting the viscoelastic properties of the polymer surface. The variation in the contact stiffness well agreed with the effective stiffness of a simple one-dimensional model, which is consistent with the fact that the maximum depth range of the technique is far beyond the extent of the contact stress field.

cond-mat.mes-hall↗

arXiv2015

Delta expansion and Wilson fermion in the Gross-Neveu model: Compatibility with linear divergence and continuum limit from inverse-mass expansion

We apply the $δ$-expansion to the Gross-Neveu model in the large $N$ limit with Wilson fermion and investigate dynamical mass generation from inverse-mass expansion. The dimensionless mass $M$ defined via the effective potential is employed as the expansion parameter of the bare coupling constant $β$ which is partially renormalized by the subtraction of linear divergence. We show that $δ$-expansion of the $1/M$ series of $β$ is compatible with the mass renormalization. After the confirmation of the continuum scaling of the bare coupling without fermion doubling, we attempt to estimate dynamical mass in the continuum limit and obtain the results converging to the exact value for values of Wilson parameter $r\in (0.8,1.0)$.

hep-lat↗

arXiv2015

Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice

In the Ising model on the simple cubic lattice, we describe the inverse temperature $β$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of those quantities are represented by the linear differential equations with constant coefficients which are related to critical exponents. We estimate the critical temperature and exponents via an expansion in the inverse powers of the mass under the use of $δ$-expansion. The critical inverse temperature $β_{c}$ is estimated first in unbiased manner and then critical exponents are also estimated in biased and unbiased self-contained way including $ω$, the correction-to-scaling exponent, $ν$, $η$ and $γ$.

hep-lat↗

arXiv2015

Delta expansion at low temperatures

In the low temperature phase of the square Ising model, we describe the inverse temperature beta as the function of a squared mass M and study the critical behavior of beta(M) via the large M expansion. Using the delta-expansion by which the large mass expansion is transformed into a series exhibiting expected scaling behavior, we perform the estimation of the critical inverse temperature beta_{c} with the help of linear differential equation to be satisfied by ansatz of beta(M) near the critical point M=0. To improve the estimation, the leading correction exponent nu is independently estimated from beta^{(2)}/beta^{(1)} and is used in the estimation of beta_{c}, giving rise to remarkable accuracy improvement.

hep-lat↗

arXiv2014

Critical exponents from large mass expansion

We perform estimation of critical exponents via large mass expansion under crucial help of delta-expansion. We address to the three dimensional Ising model at high temperature and estimate omega, the correction-to-scaling exponent, nu, eta and gamma in unbiased and self-contained manner. The results read at the highest 25th order expansion omega=0.8002, nu=0.6295, eta=0.0369 and gamma=1.2357. Estimation biased by omega=0.84(4) is also performed and proved to be in agreement with the summary of recent literatures.

hep-lat↗

arXiv2014

Large-order aspects of the delta-expansion in low-dimensional Ising models

We investigate the large order aspects of the delta-expansion under the estimation procession of the critical quantities. As illustrative examples, we revisit one-dimensional Ising model for the analytic study and two-dimensional square Ising model in the high temperature phase for the numerical experiment to large orders. In both models, proposed fundamental base on which the estimation protocol should be constructed is investigated in details and confirmed to be valid. In the square lattice model, we present a new protocol for the estimation of critical exponents and temperature.

hep-lat↗

arXiv2014

Notes on the delta-expansion approach to the 2D Ising susceptibility scaling

We study the scaling of the magnetic susceptibility in the square Ising model based upon the delta-expansion in the high temperature phase. The susceptibility chi is expressed in terms of the mass M and expanded in powers of 1/M. The dilation around M=0 by the delta expansion and the parametric extension of the ratio of derivatives of chi, chi^{(ell+1)}/chi^{(ell)} is used as a test function for the estimation of the critical exponent gamma with no bias from information of the critical temperature. Estimation is done with the help of the principle of minimum sensitivity and detailed analysis revealed that ell=0,1 cases provide us accurate estimation results. Critical exponent of the sub-leading scaling term is also estimated.

cond-mat.stat-mech↗

arXiv2013

Critical behaviors as functions of the bare-mass

In Ising model on the simple cubic lattice, we describe the inverse temperature βin terms of the bare-mass M and study its critical behavior by the use of delta expansion from high temperature or large M side. In the vicinity of critical temperature β_{c}, the expansion of βin M has β_{c} as the first term and M^{-1/2ν} as the leading correction. The estimation of β_{c} in 1/M expansion is confronted with the leading and higher order corrections, even delta expansion is applied and the critical region emerges. To improve the estimation status of β_{c}, we try to suppress the corrections by adding derivatives of β(M) with free adjustable parameters. By optimizing the parameters with the help of the principle of minimum sensitivity which are maximally imposed in accord with the number of parameters, estimation of β_{c} is carried out and the result is found to be in good agreement with the present world average. In the same time, the critical exponent ν is also estimated.

hep-lat↗

arXiv2013

Inverse Laplace transform on the lattice spacing

Inverse Laplace transform on the lattice spacing is introduced as a computational framework of the extrapolation of the strong coupling expansion to the scaling region. We apply the transform to the two-dimensional non-linear O(N) model at N>=3 and show that the approximation of the continuum limit of the susceptibility agrees with the existing theoretical and Monte Carlo data.

hep-lat↗

arXiv2012

Continuum limit of susceptibility from strong coupling expansion: Two dimensional non-linear O(N) sigma model at N>= 3

Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we express the bare coupling g in series expansion in chi. At large N, Pade-Borel approximants exhibit the scaling behavior at the four-loop level. Then, the estimation of the non-perturbative constant associated with the susceptibility is performed for N>=3 and the results are compared with the available theoretical results and Monte Carlo data.

hep-lat↗

arXiv2011

Pade-Borel approximation of the continuum limit of strong coupling lattice fields: Two dimensional non-linear O(N) sigma model at N>=3

Based on the strong coupling expansion, we reinvestigate two dimensional O(N) sigma model by the use of Pade-Borel approximants. The conventional strong coupling expansion of the mass square M in momentum space in beta=1/g^2 is inverted to give beta expanded in 1/M. Borel transform of beta with respect to M is carried out and the result is improved as the rational function by Pade method. We find the behavior of Pade-Borel transformed bare coupling at 18th order is consistent for N>=3 with that of continuum scaling to the four-loop perturbation theory. We estimate non-perturbative mass gap at N>=3 and find the agreement with the exact result by Hasenfratz et.al.

hep-lat↗

arXiv2008

Continuum scaling in expansions effective at a large lattice spacing

A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken large enough and the result gives rise to the Borel transformation with respect to the relevant variable in the lattice models. The explicit simulation of the continuum scaling from the expansion effective at large spacings is investigated in anharmonic oscillators, d=2 non-linear sigma model at large N and Gross-Neveu model with Wilson fermions.

hep-lat↗

arXiv2008

Continuum Scaling from Large Mass Expansion on the Lattice: Delta Expansion Applied to the Anharmonic Oscillator

We dilate the scaling region of the lattice anharmonic oscillator at strong coupling by introducing the parameter delta. Performing expansion in delta, the calculation of the mass gap in the continuum limit via the series expansion effective at large lattice spacings is then studied. We show that the dilation on the mass parameter M recovers the scaling behavior of the hopping parameter beta and allows for precise approximation of the mass gap.

hep-lat↗

arXiv2008

Delta Expansion on the Lattice and Dilated Scaling Region

A new kind of delta expansion is applied on the lattice to the d=2 non-linear sigma model at N=infinity and N=1 which corresponds to the Ising model. We introduce the parameter delta for the dilation of the scaling region of the model with the replacement of the lattice spacing a to (1-delta)^{1/2}a. Then, we demonstrate that the expansion in delta admits an approximation of the scaling behavior of the model at both limits of N from the information at a large lattice spacing a.

hep-lat↗

arXiv1997

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component $ϕ^4$ theory

Modified Laplace transformation method is applied to N component $ϕ^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.

hep-th↗

arXiv1997

Modified Laplace transformation method and its application to the anharmonic oscillator

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. For the non-Gaussian integral, we find that the perturbation series can give accurate result and the obtained approximation converges to the exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation expansion). In the case of anharmonic oscillator, we show that several order result yields good approximation of the ground state energy over the entire parameter space. The large order aspect is also investigated for the anharmonic oscillator.

math-ph↗

arXiv1996

Heaviside transform of the effective potential in the Gross-Neveu model

Unconventional way of handling the perturbative series is presented with the help of Heaviside transformation with respect to the mass. We apply Heaviside transform to the effective potential in the massive Gross-Neveu model and carry out perturbative approximation of the massless potential by dealing with the resulting Heaviside function. We find that accurate values of the dynamical mass can be obtained from the Heaviside function already at finite orders where just the several of diagrams are incorporated. We prove that our approximants converges to the exact massless potential in the infinite order. Small mass expansion of the effective potential can be also obtained in our approach.

hep-th↗