arXiv subjects

Do-Hyun Kim

Publications and source records attributed to Do-Hyun Kim.

5 recordsLinked to original sources

arXiv2022

Janus van der Waals equations for real molecules with two-sided phase transitions

We obtain families of generalised van der Waals equations characterised by an even number $n=2,4,6$ and a continuous free parameter which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature $T_{c}$ and arbitrarily close two critical densities. The critical phase transitions are naturally two-sided: the critical exponents are $α_{\scriptscriptstyle{P}}=γ_{\scriptscriptstyle{P}}=\frac{2}{3}$, $β_{\scriptscriptstyle{P}}=δ^{-1}=\frac{1}{3}$ for $T>T_{c}$ and $α_{\scriptscriptstyle{P}}=γ_{\scriptscriptstyle{P}}=\frac{n}{n+1}$, $β_{\scriptscriptstyle{P}}=δ^{-1}=\frac{1}{n+1}$ for $T<T_{c}$. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in low density limit. We test our formulas against NIST data for eleven major molecules and show agreements better than the original van der Waals equation, not only near to the critical points but also in low density regions.

physics.chem-ph↗

arXiv2018

Isobaric Critical Exponents: Test of Analyticity against NIST Reference Data

Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity' of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $α_{\scriptscriptstyle{P}}$, $β_{\scriptscriptstyle{P}}$ and $γ_{\scriptscriptstyle{P}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $\mathrm{H_{2}O, CO_{2}, O_{2}}$, etc. We report they are consistent with the prediction for temperature range, $10^{-5} <|T/T_{c}-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.

cond-mat.stat-mech↗

arXiv2017

Enhanced storage capacity with errors in scale-free Hopfield neural networks: an analytical study

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of $O(N)$, where $N$ is the system size. Beyond the threshold, they are completely lost. Since the introduction of the Hopfield model, the theory of neural networks has been further developed toward realistic neural networks using analog neurons, spiking neurons, etc. Nevertheless, those advances are based on fully connected networks, which are inconsistent with recent experimental discovery that the number of connections of each neuron seems to be heterogeneous, following a heavy-tailed distribution. Motivated by this observation, we consider the Hopfield model on scale-free networks and obtain a different pattern of associative memory retrieval from that obtained on the fully connected network: the storage capacity becomes tremendously enhanced but with some error in the memory retrieval, which appears as the heterogeneity of the connections is increased. Moreover, the error rates are also obtained on several real neural networks and are indeed similar to that on scale-free model networks.

cond-mat.dis-nn↗

arXiv2014

Spin-glass splitting in the quantum Ghatak-Sherrington model

We propose an expanded spin-glass model, called the quantum Ghatak-Sherrington model, which considers spin-1 quantum spin operators in a crystal field and in a transverse field. The analytic solutions and phase diagrams of this model are obtained by using the one-step replica symmetry-breaking ansatz under the static approximation. Our results represent the splitting within one spin-glass (SG) phase depending on the values of crystal and transverse fields. The two separated SG phases, characterized by a density of filled states, show certain differences in their shapes and phase boundaries. Such SG splitting becomes more distinctive when the degeneracy of the empty states of spins is larger than one of their filled states.

cond-mat.dis-nn↗

arXiv2014

Inverse transitions in a spin-glass model on a scale-free network

In this paper, we will investigate critical phenomena by considering a model spin-glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Ising-type model. Scale-free networks on which the GS model is placed are constructed from the static model, in which the number of vertices is fixed from the beginning. On the basis of the replica-symmetric solution, we obtain the analytical solutions, i.e., free energy and order parameters, and we derive the various phase diagrams consisting of the paramagnetic, ferromagnetic, and spin glass phases as functions of temperature $T$, the degree exponent $λ$, the mean degree $K$, and the fraction of the ferromagnetic interactions $ρ$. Since the present model is based on the GS model, which considers the three states ($S=0, \pm 1$), the $S=0$ state plays a crucial role in the $λ$-dependent critical behavior: glass transition temperature $T_{g}$ has a finite value, even when $2 < λ< 3$. In addition, when the crystal field becomes nonzero, the present model clearly exhibits three types of inverse transitions, which occur when an ordered phase is more entropic than a disordered one.

cond-mat.dis-nn↗