Zero-temperature phase transitions and their anomalous influence on thermodynamic behavior in the q-state Potts model on a diamond chain.

The q-state Potts model on a diamond chain has mathematical significance in analyzing phase transitions and critical behaviors in diverse fields, including statistical physics, condensed matter physics, and materials science. By focusing on the three-state Potts model on a diamond chain, we reveal rich and analytically solvable behaviors without phase transitions at finite temperatures. Upon investigating thermodynamic properties such as internal energy, entropy, specific heat, and correlation length, we observe sharp changes near zero temperature. Magnetic properties, including magnetization and magnetic susceptibility, display distinct behaviors that provide insights into spin configurations in different phases. However, the Potts model lacks genuine phase transitions at finite temperatures, in line with the Peierls argument for one-dimensional systems. Nonetheless, in the general case of an arbitrary q state, magnetic properties such as correlation length, magnetization, and magnetic susceptibility exhibit intriguing remnants of a zero-temperature phase transition at finite temperatures. Furthermore, residual entropy uncovers unusual frustrated regions at zero-temperature phase transitions. This feature leads to the peculiar thermodynamic properties of phase boundaries, including a sharp entropy change resembling a first-order discontinuity without an entropy jump, and pronounced peaks in second-order derivatives of free energy, suggestive of a second-order phase transition divergence but without singularities. This unusual behavior is also observed in the correlation length at the pseudocritical temperature, which could potentially be misleading as a divergence.

Residual entropy of the dilute Ising chain in a magnetic field.

The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged nonmagnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy, and magnetization for the ground state phases. We prove the absence of pseudotransitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.

Hairy Roots of Scutellaria spp. (Lamiaceae) as Promising Producers of Antiviral Flavones.

We measured and studied the growth parameters and the qualitative and quantitative composition of the flavones of hairy roots of the Scutellaria genus: S. lateriflora, S. przewalskii and S. pycnoclada. Hairy roots were obtained using wild-type Agrobacterium rhizogenes A4 by co-cultivation of explants (cotyledons) in a suspension of Agrobacterium. The presence of the rol-genes was confirmed by PCR analysis. The hairy roots of the most studied plant from the Scutellaria genus, S. baicalensis, were obtained earlier and used as a reference sample. HPLC-MS showed the predominance of four main flavones (baicalin, baicalein, wogonin and wogonoside) in the methanol extracts of the studied hairy roots. In addition to the four main flavones, the other substances which are typical to the aerial part of plants were found in all the extracts: apigenin, apigetrin, scutellarin and chrysin-7-O-ß-d-glucuronide. According to the total content of flavones, the hairy roots of the studied skullcaps form the following series: S. przewalskii (33 mg/g dry weight) > S. baicalensis (17.04 mg/g dry weight) > S. pycnoclada (12.9 mg/g dry weight) > S. lateriflora (4.57 mg/g dry weight). Therefore, the most promising producer of anti-coronavirus flavones is S. przewalskii.

Unconventional low-temperature features in the one-dimensional frustrated q-state Potts model.

Here we consider a one-dimensional q-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit strong acute peaks similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where this anomalous feature occurs we call the pseudocritical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudocritical exponents that satisfy a class of universality previously identified in the literature for other one-dimensional models; these pseudocritical exponents are for correlation length ν=1, specific heat α=3, and magnetic susceptibility µ=3.