Related papers: Residual Entropy of Ice: A Study Based on Transfer…
The long-standing question of whether the residual entropy of hexagonal ice ($S_h$) equals that of cubic ice ($S_c$) remains unresolved despite decades of research on ice-type models. While analytical studies have established the inequality…
We estimated the residual entropy of ice Ih by the recently developed simulation protocol, namely, the combination of Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method. We employed a model with the nearest…
We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both for the case that in zero magnetic field and that in an imaginary magnetic field i({\pi}/2)kT. The spin configurations of this…
Among the many ice polymorphs, ice I, that is present in nature at ambient pressure, occurs with two different structures, i.e. the stable hexagonal (Ih) or the metastable cubic (Ic) one. An accurate analysis of cubic ice Ic was missing…
The configurational entropy of ice is calculated by thermodynamic integration from high to low temperatures. We use Monte Carlo simulations with a simple energy model which reproduces the Bernal-Fowler ice rules. This procedure is found to…
We introduce two simple models with nearest neighbor interactions on 3D hexagonal lattices. Each model allows one to calculate the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. This gives the correction to…
The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…
In this text, we implement a monte carlo algorithm to study thermodynamic properties of ice. Our program, written in Python, is open-sourced and available at https://github.com/AKnightWing/ColdAsIce. We develop a novel scheme to compute the…
The residual entropy of spin ice and other frustrated magnets is a property of considerable interest, yet the usual way of determining it, by integrating the heat capacity, is generally ambiguous. Here we note that a straightforward…
In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for…
Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing…
While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show…
Residual entropy, which reflects the degrees of freedom in a system at absolute zero temperature, is crucial for understanding quantum and classical ground states. Despite its key role in explaining low-temperature phenomena and ground…
The fundamental properties of ice have always attracted a lot of interest due to omnipresence of ice in many different natural contexts. Since cubic ice recently become experimentally accessible from a low-density gas hydrate precursor [1,…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…
The configurational entropy of several H-disordered ice polymorphs is calculated by means of a thermodynamic integration along a path between a totally H-disordered state and one fulfilling the Bernal-Fowler ice rules. A Monte Carlo…
Recently pseudo-critical temperature clues were observed in one-dimensional spin models, such as the Ising-Heisenberg spin models, among others. Here we report a relationship between the zero-temperature phase boundary residual entropy…
Although the third law of thermodynamics was established almost a century ago, it is not yet universally considered to be a fundamental law of physics. A major problem is that there are many materials having residual entropy. Amorphous…
Hexagonal ice ($\rm{I_h}$), the most common structure of ice, displays a variety of fascinating properties. Despite major efforts, a theoretical description of all its properties is still lacking. In particular, correctly accounting for its…
Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate)…