Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur

Functional relations for the six vertex model with domain wall boundary conditions

In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied for small lattices and the properties determining the partition function are also discussed.Comment: 19 pages, v2: typos corrected, new section and appendix added. v3: minor corrections, to appear in J. Stat. Mech

Boundary correlation functions of the six-vertex model

We consider the six-vertex model on an $N \times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known result for the partition function. In the free fermion case the explicit answers are obtained. The introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings.Comment: 20 pages, 2 figures, typos correcte

On the partition function of the six-vertex model with domain wall boundary conditions

The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ``reconstruction'' formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.Comment: typos correcte

Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques

The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics of random matrix techniques, the connections to the polynuclear growth models and a method using the Green's function.Comment: 41 pages, 10 figures, minor corrections, references adde

Photodynamic inactivation of mammalian viruses and bacteriophages

Photodynamic inactivation (PDI) has been used to inactivate microorganisms through the use of photosensitizers. The inactivation of mammalian viruses and bacteriophages by photosensitization has been applied with success since the first decades of the last century. Due to the fact that mammalian viruses are known to pose a threat to public health and that bacteriophages are frequently used as models of mammalian viruses, it is important to know and understand the mechanisms and photodynamic procedures involved in their photoinactivation. The aim of this review is to (i) summarize the main approaches developed until now for the photodynamic inactivation of bacteriophages and mammalian viruses and, (ii) discuss and compare the present state of the art of mammalian viruses PDI with phage photoinactivation, with special focus on the most relevant mechanisms, molecular targets and factors affecting the viral inactivation process.publishe

Optical Nanoantennas for Multiband Surface-Enhanced Infrared and Raman Spectroscopy

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