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We investigate the RG domain wall between neighboring $A_2^{(p)}$ minimal CFT models and establish the map between UV and IR fields (matrix of mixing coefficients). A particular RG invariant set of six primary and four descendant fields is analyzed in full details. Using the algebraic construction of the RG domain wall we compute the UV/IR mixing matrix. To test our results we show that it diagonalizes the matrix of anomalous dimensions previously known from perturbative analysis. It is important to note that the diagonalizing matrix can not be found from perturbative analysis solely due to degeneracy of anomalous dimensions. The same mixing coefficients are used to explore anomalous W-weights as well., Comment: 25 pages

The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in terms of the anisotropy parameter is found. We calculate the next to leading $\sim 1/N^2$ corrections to the spectrum on both lattice theory and the perturbed CFT sides for several classes of states, always getting exact agreement. We discuss also how the perturbing operators and the higher integrals of motion are related., Comment: 18 pages, 3 figures, published version, a comment and a reference added

The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the system, along non-contractible circles of the cylinder, before closing it into a torus. We derive exact expressions for the eigenvalues of the transfer matrix for the critical ferromagnetic Ising model on the M x N square lattice wrapped on the torus with a specific defect line. As result we have obtained analytically the partition function for the Ising model with such boundary conditions. In the case of infinitely long cylinders of circumference L with duality twisted boundary conditions we obtain the asymptotic expansion of the free energy and the inverse correlation lengths. We find that the ratio of subdominant finite-size correction terms in the asymptotic expansion of the free energy and the inverse correlation lengths should be universal. We verify such universal behavior in the framework of perturbating conformal approach by calculating the universal structure constant Cn1n for descendent states generated by the operator product expansion (OPE) of the primary fields. For such states the calculations of the universal structure constants is difficult task, since its involve the knowledge of the four-point correlation function, which in general does not fix by conformal invariance except for some particular cases, including the Ising model., Comment: 37 pages, 5 figures

The critical Ising model in two dimensions with a defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically the partition function and the asymptotic expansions of the free energy and inverse correlation lengths for an infinitely long cylinder of circumference $L_x$. We find that finite-size corrections to scaling are of the form $a_k/L^{2k-1}_x$ for the free energy $f$ and $b_k(p)/L_x^{2k-1}$ and $c_k(p)/L_x^{2k-1}$ for inverse correlation lengths $\xi^{-1}_p$ and $\xi^{-1}_{L-p}$, respectively, with integer values of $k$. By exact evaluation we find that the amplitude ratios $b_k(p)/a_k$ and $c_k(p)/a_k$ are universal and verify this universal behavior using a perturbative conformal approach., Comment: 5 pages, 5 figures, added Acknowledgments

We extend the analysis of the RG trajectory connecting successive minimal CFT models ${\cal M}_p$ and ${\cal M}_{p-1}$ for $p\gg 1$, performed by A. Zamolodchikov, to the fields $\varphi_{n,n\pm 3}$. This required a close investigation of mixing with the descendant fields at the level 2. In particular we identify those specific linear combinations of UV fields which flow to the IR fields $\varphi_{n+3,n}$ and $\varphi_{n-3,n}$. We report also the results of the calculation of the same mixing coefficients through the recent RG domain wall approach by Gaiotto. These results are in complete agreement with the leading order perturbation theory., Comment: 13 pages; minor corrections; version published in JHEP

The salt fraction in permafrost soils/sediments of the McMurdo Dry Valleys (MDV) of Antarctica can be used as a proxy for cold desert geochemical processes and paleoclimate reconstruction. Previous analyses of the salt fraction in MDV permafrost soils have largely been conducted in coastal regions where permafrost soils are variably affected by aqueous processes and mixed inputs from marine and stratospheric sources. We expand upon this work by evaluating permafrost soil/sediments in University Valley, located in the ultraxerous zone where both liquid water transport and marine influences are minimal. We determined the abundances of Cl(-), NO3(-, ClO4(-)and ClO3(-)in dry and ice-cemented soil/sediments, snow and glacier ice, and also characterized Cl(-) and NO3(-) isotopically. The data are not consistent with salt deposition in a sublimation till, nor with nuclear weapon testing fall-out, and instead point to a dominantly stratospheric source and to varying degrees of post depositional transformation depending on the substrate, from minimal alteration in bare soils to significant alteration (photodegradation and/or volatilization) in snow and glacier ice. Ionic abundances in the dry permafrost layer indicate limited vertical transport under the current climate conditions, likely due to percolation of snowmelt. Subtle changes in ClO4(-)/NO3(-) ratios and NO3(-) isotopic composition with depth and location may reflect both transport related fractionation and depositional history. Low molar ratios of ClO3(-)/ClO4(-) in surface soils compared to deposition and other arid systems suggest significant post depositional loss of ClO3(-), possibly due to reduction by iron minerals, which may have important implications for oxy-chlorine species on Mars. Salt accumulation varies with distance along the valley and apparent accumulation times based on multiple methods range from approximately 10 to 30 kyr near the glacier to 70-200 kyr near the valley mouth. The relatively young age of the salts and relatively low and homogeneous anion concentrations in the ice-cemented sediments point to either a mechanism of recent salt removal, or to relatively modern permafrost soils (less than 1 million years). Together, our results show that near surface salts in University Valley serve as an end-member of stratospheric sources not subject to biological processes or extensive remobilization.