Coupling of hard dimers to dynamical lattices via random tensors

We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the critical behavior of the continuum limit is the one of pure random lattices. We find a negative critical activity where the universality class is changed as dimers become critical, in a very similar way hard dimers exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents are calculated exactly. An alternative description as a system of `color-sensitive hard-core dimers' on random branched polymers is provided.Comment: 12 page

The 1/N expansion of colored tensor models

In this paper we perform the 1/N expansion of the colored three dimensional Boulatov tensor model. As in matrix models, we obtain a systematic topological expansion, with more and more complicated topologies suppressed by higher and higher powers of N. We compute the first orders of the expansion and prove that only graphs corresponding to three spheres S^3 contribute to the leading order in the large N limit.Comment: typos corrected, references update

Revisiting random tensor models at large N via the Schwinger-Dyson equations

The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable ensemble) is a specific generalization of the Virasoro algebra and it is important to show that these new symmetries determine the physical solutions. We prove this result for random tensors at large N. Compared to matrix models, tensor models have more than a single invariant at each order in the tensor entries and the SDEs make them proliferate. However, the specific combinatorics of the dominant observables allows to restrict to linear SDEs and we show that they determine a unique physical perturbative solution. This gives a new proof that tensor models are Gaussian at large N, with the covariance being the full 2-point function.Comment: 17 pages, many figure

The complete 1/N expansion of colored tensor models in arbitrary dimension

In this paper we generalize the results of [1,2] and derive the full 1/N expansion of colored tensor models in arbitrary dimensions. We detail the expansion for the independent identically distributed model and the topological Boulatov Ooguri model

A comparative study of austenitic structure in NiTi and Fe based shape memory alloys after severe plastic deformation

The effect of high speed high pressure torsion (HS-HPT) was studied in NiTi and FeMnSiCr SMAs, by comparison. Severe plastic deformation was performed in austenite state for both types of alloys. The alloys subjected to HS-HPT, reduced their grain size due to microstructure fragmentation by compression and torsion. The active elements were achieved being able to support variable ranges of processing parameters like force, pressure, rotation speed and time of torsion. The evolution of microstructural refinement in the samples subjected to different deformation by HS-HPT, were studied by optical and scanning electron microscopy observation and the thermal effect was reveled using differential scanning calorimetry (DSC). (C) 2015 The Authors. Published by Elsevier Ltd.publishersversionpublishe

The 1/N expansion of colored tensor models in arbitrary dimension

In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S^D contribute to the leading order in the large N limit.Comment: 4 pages, 3 figure

Topological Graph Polynomials in Colored Group Field Theory

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph \cG_{\partial} of an open graph \cG and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension

EPRL/FK Group Field Theory

The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model.Comment: 20 pages, 2 figure

Quantum widening of CDT universe

The physical phase of Causal Dynamical Triangulations (CDT) is known to be described by an effective, one-dimensional action in which three-volumes of the underlying foliation of the full CDT play a role of the sole degrees of freedom. Here we map this effective description onto a statistical-physics model of particles distributed on 1d lattice, with site occupation numbers corresponding to the three-volumes. We identify the emergence of the quantum de-Sitter universe observed in CDT with the condensation transition known from similar statistical models. Our model correctly reproduces the shape of the quantum universe and allows us to analytically determine quantum corrections to the size of the universe. We also investigate the phase structure of the model and show that it reproduces all three phases observed in computer simulations of CDT. In addition, we predict that two other phases may exists, depending on the exact form of the discretised effective action and boundary conditions. We calculate various quantities such as the distribution of three-volumes in our model and discuss how they can be compared with CDT.Comment: 19 pages, 13 figure

Establishing the Constitutive Law of a CrMo Alloyed Steel

The paper shows the results of the researches for establishing the equation of the deformation behavior of alloyed steel with chromium and molybdenum. The behavior law is established in the experimental way, using the results of a set of torsion tests. The composed constitutive law had very good experimental verification