Attempted Bethe ansatz solution for one-dimensional directed polymers in random media

We study the statistical properties of one-dimensional directed polymers in a short-range random potential by mapping the replicated problem to a many body quantum boson system with attractive interactions. We find the full set of eigenvalues and eigenfunctions of the many-body system and perform the summation over the entire spectrum of excited states. The analytic continuation of the obtained exact expression for the replica partition function from integer to non-integer replica parameter N turns out to be ambiguous. Performing the analytic continuation simply by assuming that the parameter N can take arbitrary complex values, and going to the thermodynamic limit of the original directed polymer problem, we obtain the explicit universal expression for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur

Magnetocrystalline anisotropy of the multiphase samples of the hexaferrites Ba2Ni2-xCuxFe12O22 studied by the ferromagnetic resonance method

This paper presents structural and magnetic investigation of the hexaferrites Ba2Ni2-xCuxFe12O22 system in the Cu2+ concentration range 0 ≤ x ≤ 1.4. Samples were synthesized according to traditional ceramic processing technology. The samples were multiphase, since the optimal conditions of synthesis were not specially worked out. According to the data of X-ray diffraction analysis, the samples contain both a target phase and impurity phases of magnetite and hematite, as well as hexagonal phase of Ba-M. The values of the saturation magnetization of the samples were a little more than the values in the literature. It could be explained by the contribution from impurity phases with large magnetization values. The values of the anisotropy fields of the separate phases, which are contained in the investigated samples, were determined by the method of ferromagnetic resonance. The anisotropy field decreases with an increase in the content of copper ion. It is show that the value of the anisotropy field of hexaferrite Ni2Y is close to the literature value

Summability of the perturbative expansion for a zero-dimensional disordered spin model

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure

Static and dynamic magnetic properties of polycrystalline hexaferrites of the Ba2Ni2-xCuxFe12O22 system

The paper presents the results of a study of the phase composition and the main static magnetic characteristics: saturation magnetization, residual magnetization and coercive force of polycrystalline ferroxplana type hexaferrites of the Ba2Ni2-xCuxFe12O22 (0 < x < 2.0) system. These materials have high magnetic permeability and are promising for use as substrates for magnetic antennas and radar absorbing materials. It is shown that thermograms of the initial permeability can be used to quickly assess the presence of impurity magnetic phases in complex oxide ferrimagnets. The permeability and permittivity spectra of textured and non-textured composite samples with the powder of the Ba2NiCuFe12O22 hexaferrite are measured in the microwave frequency range. The radar absorbing properties of the obtained composites are analyzed. It is shown that magnetic texturing leads to an increase in the operating frequency band of an absorber with RL < -10 dB from 6.1 GHz to 8.2 GHz and a deepening of the loss minimum from -21 dB to -27 dB

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure