arXiv subjects

Marcelo M. Leite

Publications and source records attributed to Marcelo M. Leite.

At least 19 recordsLinked to original sources

arXiv2023

The simplest minimal subtraction for massive scalar field theory

The simplest minimal subtraction method for massive λϕ4 scalar field theory is presented. We utilize the one-particle irreducible vertex parts framework to deal only with the primitive divergent ones that can be renormalized multiplicatively. We give a unified description for spacetime metric tensor with either Minkowski or Euclidean signature.The partial-p operation in the remaining diagrams of the two-point vertex part are used to get rid of its overlapping divergences. We show how the parametric dissociation transform effectively eliminates the external momentum dependence of the coefficient of the squared bare mass after performing the partial-p operation in the two-point vertex part diagrams. The resemblance of this method with a minimal subtraction scheme in the massless theory is pointed out. We derive the Callan-Symanzik equations using minimal subtraction arguments and discuss the scaling limit in the ultraviolet region. We apply the method to determine critical exponents for an O(N) internal symmetry at least up to two-loop order with a flat Euclidean metric and find perfect agreement with all previous results in the literature.

hep-th↗

arXiv2021

Generic anisotropic Lifshitz scalar field theory: masslesslike massive minimal subtraction

We formulate the simplest minimal subtraction version for massive $λϕ^4$ scalar fields with $O(N)$ symmetry for generic anisotropic Lifshitz space-times. An appropriate partial$-p$ operation is applied in the bare two-point vertex function diagrams, which separates the original diagram into a sum of two different integrals which are the coefficients of the corresponding polynomials in the mass and external momentum. Within the proposed method, the coefficient of the mass terms can be discarded and we obtain a minimal subtraction method almost identical to the same scheme in the massless theory in {\it every external momentum/mass subspace}. We restrict our demonstration of the method up to three-loop order in the two-point vertex part. We verify the consistency of our method by a diagrammatic computation of static critical exponents, which validates the universality hypothesis.

hep-th↗

arXiv2021

Masslesslike minimal subtraction for massive scalar field theory

We introduce the simplest minimal subtraction method for massive $λϕ^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the partial-$p$ operation in every diagram of the two-point vertex part in order to separate it into a sum of squared mass and external momentum, respectively, with different coefficients. Then, the loop integral which is the coefficient of the quadratic mass can be solved entirely in terms of the mass, no longer depending upon the external momentum, using the {\it parametric dissociation transform}. It consists in the choice of a certain set of fixed values of Feynman parameters replaced inside the remaining loop integral after solving the internal subdiagrams. We check the results in the diagrammatic computation of critical exponents at least up to two-loop order using a flat metric with Euclidean signature.

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arXiv2017

Neumann boundary conditions with null external quasi-momenta in finite-systems

The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study the critical behavior of such a system. The renormalized vertex parts are defined at zero external quasi-momenta, which makes the analysis particularly simple. The distance between the boundary plates $L$ characterizing the finite size system direction perpendicular to the hyperplanes plays a similar role here in comparison with our recent unified treatment for Neumann and Dirichlet boundary conditions. Critical exponents are computed using diagrammatic expansion at least up to two-loop order and are shown to be identical to those from the bulk theory (limit $L \rightarrow \infty$).

cond-mat.stat-mech↗

arXiv2017

Chiral Closed strings: Four massless states scattering amplitude

We compute the scattering amplitudes of four massless states for chiral (closed) bosonic and type II superstrings using the Kawai-Lewellen-Tye ($KLT$) factorization method. The amplitude in the chiral bosonic case is identical to a field theory amplitude corresponding to the spin-$2$ tachyon, massless gravitational sector and massive spin-2 tardyon states of the spectrum. Chiral type II superstrings amplitude only possess poles associated with the massless gravitational sector. We briefly discuss the extension of the calculation to heterotic superstrings.

hep-th↗

arXiv2017

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann: massive scalar theory and critical exponents

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar $λϕ^{4}$ theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents $η$ and $ν$ at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann ($BPHZ$) method at the same loop order, show that the proposed method requires fewer diagrams and establish a connection between the two approaches.

hep-th↗

arXiv2016

Modern finite-size criticality: Dirichlet and Neumann boundary conditions

Finite-size critical systems defined on a parallel plate geometry of finite extent along one single ($z$) direction with Dirichlet and Neumann boundary conditions at $z=0,L$ are analyzed in momentum space. We introduce a modified representation for the discrete eigenfunctions in a renormalized one-particle irreducible vertex part ($1PI$) scalar field-theoretic framework using either massless or massive fields. The appearance of multiplicities in the Feynman rules to construct diagrams due to this choice of representation of the basis functions is discussed along with the modified normalization conditions. For nonvanishing external quasi-momenta, Dirichlet and Neumann boundary conditions are shown to be unified within a single formalism. We examine the dimensional crossover regimes for these and show a correspondence with those from antiperiodic and periodic boundary conditions. It is demonstrated that finite-size effects for Dirichlet and Neumann boundary conditions do not require surface fields necessarily but are implemented nontrivially from the Feynman rules involving only bulk terms in the Lagrangian. As an application, the critical exponents $η$ and $ν$ are evaluated at least up to two-loop level through diagrammatic means. We show that the critical indices are the same as those from the bulk (infinite) system irrespective of the boundary conditions.

cond-mat.stat-mech↗

arXiv2014

Massive minimal subtraction scheme and "partial-$p$" in anisotropic Lifshitz space(time)s

We introduce the "partial-$p$" operation in a massive Euclidean $λϕ^{4}$ scalar field theory describing anisotropic Lifshitz critical behavior. We then develop a minimal subtraction a la $Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an application we compute critical exponents diagrammatically using the orthogonal approximation at least up to two-loop order and show their equivalence with other renormalization techniques. We discuss possible applications of the method in other field-theoretic contexts.

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arXiv2011

Susceptibility amplitude ratio for generic competing systems

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with $L$ independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of $m$-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.

cond-mat.stat-mech↗

arXiv2011

Critical exponents from parallel plate geometries subject to periodic and antiperiodic boundary conditions

We introduce a renormalized 1PI vertex part scalar field theory setting in momentum space to computing the critical exponents $ν$ and $η$, at least at two-loop order, for a layered parallel plate geometry separated by a distance L, with periodic as well as antiperiodic boundary conditions on the plates. We utilize massive and massless fields in order to extract the exponents in independent ultraviolet and infrared scaling analysis, respectively, which are required in a complete description of the scaling regions for finite size systems. We prove that fixed points and other critical amounts either in the ultraviolet or in the infrared regime dependent on the plates boundary condition are a general feature of normalization conditions. We introduce a new description of typical crossover regimes occurring in finite size systems. Avoiding these crossovers, the three regions of finite size scaling present for each of these boundary conditions are shown to be indistinguishable in the results of the exponents in periodic and antiperiodic conditions, which coincide with those from the (bulk) infinite system.

cond-mat.stat-mech↗

arXiv2009

Callan-Symanzik-Lifshitz approach to generic competing systems

We present the Callan-Symanzik-Lifshitz method to approaching the critical behaviors of systems with arbitrary competing interactions. Every distinct competition subspace in the anisotropic cases define an independent set of renormalized vertex parts via normalization conditions with nonvanishing distinct masses at zero external momenta. Otherwise, only one mass scale is required in the isotropic behaviors. At the critical dimension, we prove: i) the existence of the Callan-Symanzik-Lifshitz equations and ii) the multiplicative renormalizability of the vertex functions using the inductive method. Away from the critical dimension, we utilize the orthogonal approximation to compute higher loop Feynman integrals, anisotropic as well as isotropic, necessary to get the exponents $η_{n}$ and $ν_{n}$ at least up to two-loop level. Moreover, we calculate the latter exactly for isotropic behaviors at the same perturbative order. Similarly to the computation in the massless formalism, the orthogonal approximation is found to be exact at one-loop order. The outcome for all critical exponents matches exactly with those computed using the zero mass field-theoretic description renormalized at nonvanishing external momenta.

hep-th↗

arXiv2007

Callan-Symanzik method for $m$-axial Lifshitz points

We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero external momenta. The orthogonal approximation is employed to obtain the critical indices $η_{L2}$, $ν_{L2}$, $η_{L4}$ and $ν_{L4}$ diagramatically at least up to two-loop order in the anisotropic criticalities. This approximation is also utilized to compute the exponents $η_{L4}$ and $ν_{L4}$ in the isotropic case. Furthermore, we compute those exponents exactly for the isotropic behaviors at the same loop order. The results obtained for all exponents are in perfect agreement with those previously derived in the massless theories renormalized at nonzero external momenta.

hep-th↗

arXiv2005

Critical behavior of generic competing systems

Generic higher character Lifshitz critical behaviors are described using field theory and $ε_{L}$-expansion renormalization group methods. These critical behaviors describe systems with arbitrary competing interactions. We derive the scaling relations and the critical exponents at the two-loop level for anisotropic and isotropic points of arbitrary higher character. The framework is illustrated for the $N$-vector $ϕ^{4}$ model describing a $d$-dimensional system. The anisotropic behaviors are derived in terms of many independent renormalization group transformations, each one characterized by independent correlation lengths. The isotropic behaviors can be understood using only one renormalization group transformation. Feynman diagrams are solved for the anisotropic behaviors using a new dimensional regularization associated to a generalized orthogonal approximation. The isotropic diagrams are treated using this approximation as well as with a new exact technique to compute the integrals. The entire procedure leads to the analytical solution of generic loop order integrals with arbitrary external momenta. The property of universality class reduction is also satisfied when the competing interactions are turned off. We show how the results presented here reduce to the usual $m$-fold Lifshitz critical behaviors for both isotropic and anisotropic criticalities.

cond-mat.stat-mech↗

arXiv2004

New universality classes for generic higher character Lifshitz points

We describe new universality classes associated to generic higher character Lifshitz critical behaviors for systems with arbitrary short range competing interactions. New renormalization-group arguments are proposed for anisotropic and isotropic systems. The usual $m$-axial Lifshitz universality classes are obtained as a simple limit of this arbitrary competing critical behavior.

cond-mat.stat-mech↗

arXiv2003

Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"

We reply to a recent comment by Diehl and Shpot (cond-mat/0305131) criticizing a new approach to the Lifshitz critical behavior just presented (M. M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of inconsistencies in the ultraviolet regime. We recall that the orthogonal approximation employed to solve arbitrary loop diagrams worked out at the criticized paper even at three-loop level is consistent with homogeneity for arbitrary loop momenta. We show that the criticism is incorrect.

cond-mat.stat-mech↗

arXiv2003

Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors

We determine the specific heat amplitude ratio near a $m$-axial Lifshitz point and show its universal character. Using a recent renormalization group picture along with new field-theoretical $ε_{L}$-expansion techniques, we established this amplitude ratio at one-loop order. We estimate the numerical value of this amplitude ratio for $m=1$ and $d=3$. The result is in very good agreement with its experimental measurement on the magnetic material $MnP$. It is shown that in the limit $m \to 0$ it trivially reduces to the Ising-like amplitude ratio.

cond-mat.stat-mech↗

arXiv2002

A new picture of the Lifshitz critical behavior

New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8) situations. The general theory is illustrated for the N-vector phi^4 model describing a d-dimensional system. A new regularization and renormalization procedure is presented for both types of Lifshitz behavior. The anisotropic cases are formulated with two independent renormalization group transformations. The description of the isotropic behavior requires only one type of renormalization group transformation. We point out the conceptual advantages implicit in this picture and show how this framework is related to other previous renormalization group treatments for the Lifshitz problem. The Feynman diagrams of arbitrary loop-order can be performed analytically provided these integrals are considered to be homogeneous functions of the external momenta scales. The anisotropic universality class (N,d,m) reduces easily to the Ising-like (N,d) when m=0. We show that the isotropic universality class (N,m) when m is close to 8 cannot be obtained from the anisotropic one in the limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in good agreement with recent Monte Carlo simulations for the ANNNI model.

cond-mat.stat-mech↗

arXiv2002

New renormalization group approach and scaling laws for the Lifshitz critical behavior

A new renormalization group treatment is proposed for the critical exponents of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are described by two independent fixed points associated to two independent momentum flow along the quadratic and quartic directions, respectively. The isotropic case is described separately. In that case, the fixed point is due to renormalization group transformations along the quartic directions. The new scaling laws are derived for both cases and generalize the ones previously reported.

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