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T. Takagi

Publications and source records attributed to T. Takagi.

60 records · Page 4Linked to original sources
arXiv2001

Premartensitic Transition in Ni2+xMn1-xGa Heusler Alloys

The temperature dependencies of the resistivity and magnetization of a series of Ni2+XMn1-XGa (X = 0 - 0.09) alloys were investigated. Along with the anomalies associated with ferromagnetic and martensitic transitions, well-defined anomalies were observed at the temperature of premartensitic transformation. The premartensitic phase existing in a temperature range 200 - 260 K in the stoichiometric Ni2MnGa is suppressed by the martensitic phase with increasing Ni content and vanishes in Ni2.09Mn0.91Ga composition.

cond-mat.mtrl-sci↗
arXiv2001

Paths, Crystals and Fermionic Formulae

We introduce a fermionic formula associated with any quantum affine algebra U_q(X^{(r)}_N). Guided by the interplay between corner transfer matrix and Bethe ansatz in solvable lattice models, we study several aspects related to representation theory, most crucially, the crystal basis theory. They include one dimensional sums over both finite and semi-infinite paths, spinon character formulae, Lepowski-Primc type conjectural formula for vacuum string functions, dilogarithm identities, Q-systems and their solution by characters of various classical subalgebras and so forth. The results expand [HKOTY1] including the twisted cases and more details on inhomogeneous paths consisting of non-perfect crystals. As a most intriguing example, certain inhomogeneous one dimensional sums conjecturally give rise to branching functions of an integrable G^{(1)}_2-module related to the embedding G^{(1)}_2 \hookrightarrow B^{(1)}_3 \hookrightarrow D^{(1)}_4.

math.QA↗
arXiv2001

Scattering rules in soliton cellular automata associated with crystal bases

Solvable vertex models in a ferromagnetic regime give rise to soliton cellular automata at q=0. By means of the crystal base theory, we study a class of such automata associated with the quantum affine algebra U_q(g_n) for non exceptional series g_n = A^{(2)}_{2n-1}, A^{(2)}_{2n}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}. They possess a commuting family of time evolutions and solitons labeled by crystals of the smaller algebra U_q(g_{n-1}). Two-soliton scattering rule is identified with the combinatorial R of U_q(g_{n-1})-crystals, and the multi-soliton scattering is shown to factorize into the two-body ones.

math.QA↗
arXiv1997

Crystals for Demazure Modules of Classical Affine Lie Algebras

We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types $A^{(1)}_n,B^{(1)}_n,C^{(1)}_n,D^{(1)}_n, A^{(2)}_{2n-1},A^{(2)}_{2n}, and D^{(2)}_{n+1}$. We find a special sequence of affine Weyl group elements for the selected perfect crystal, and show if the highest weight is $l\La_0$, the Demazure crystal has a remarkably simple structure.

q-alg↗
arXiv1997

Characters of Demazure modules and solvable lattice models

We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one dimensional configurations which we call unrestricted, classically restricted and restricted paths. As an application characters of Demazure modules are obtained in terms of $q$-multinomial coefficients for several level 1 modules of classical affine algebras.

q-alg↗