arXiv subjects

Szabolcs Varga

Publications and source records attributed to Szabolcs Varga.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamic and structural behavior of one-dimensional divalent patchy hard rods: Wertheim's first-order thermodynamic perturbation theory vs exact results

We investigate the thermodynamic and structural properties of divalent patchy hard rods confined to a one-dimensional channel by modeling the bonding sites as attractive square-well (SW) patches located at the rod tips. The zero-range sticky limit is recovered by letting the well width vanish while keeping the stickiness parameter finite. While Wertheim's first-order thermodynamic perturbation theory becomes exact in this sticky limit, it fails for finite-range site--site interactions. Because the present model is mathematically equivalent to an exactly solvable one-dimensional nearest-neighbor fluid, we use the exact solution to reformulate the thermodynamics in terms of association-theory variables, including the fraction of unbonded sites and a generalized law of mass action. Finite-range SW sites produce a richer structural behavior than sticky sites, including monotonic and oscillatory asymptotic decay of the pair correlation function, separated by the Fisher--Widom line. In the monotonic regime, the correlation length exhibits an absolute maximum defining the Widom line, while in the oscillatory regime it may display a local maximum and minimum, whose locus defines the ``Extrema of the Correlation length under Oscillatory decay'' line. These features disappear in the sticky limit, where the system remains entirely in the oscillatory regime. We also show that the high-pressure behavior of the correlation length changes from $ξ\sim p^2$ for finite-range SW sites to $ξ\sim p^3$ in the sticky limit.

cond-mat.soft↗

arXiv2026

Structural crossovers of quasi-one-dimensional patchy hard superellipses

We study a quasi-one-dimensional associating fluid composed of hard superellipses carrying two patches interacting through a directional Kern--Frenkel potential. Using the Transfer Operator Method, we show that the selective patch--patch association promotes horizontal alignment and chain formation at low-to-intermediate densities, whereas hard-core interaction favours vertical alignment without bonds at high densities. The competition between these two mechanisms drives a structural crossover upon compression from a horizontally aligned bonded chain structure to a completely unbonded, vertically aligned structure. While patchy ellipses undergo a tilted-to-vertical realignment, patchy rectangle-like superellipses exhibit a horizontal-to-vertical change. These structural changes manifest as a plateau in the equation of state. To capture these properties, we generalise Wertheim's first-order thermodynamic perturbation theory by introducing an orientation-dependent fraction of sites not in a bond. When combined with the Parsons--Lee hard-body theory, the orientationally resolved perturbation theory provides quantitatively reliable results for the structural properties and phase behaviour. Therefore, the generalised Wertheim theory together with Parsons-Lee theory can be suitable in higher dimensions, too.

cond-mat.soft↗

arXiv2026

Orientational ordering and correlations in a quasi-one-dimensional hard-dumbbell fluid

We study a quasi-one-dimensional fluid of hard dumbbells with continuous orientational degrees of freedom using an exact transfer-matrix formulation. The model allows for a complete analytical characterization of thermodynamic properties, orientational ordering, and correlation functions in terms of the spectral properties of an integral operator. We derive exact expressions for the equation of state, the orientational distribution function, and both partial and total radial distribution functions. Their asymptotic behavior is governed by the complex poles of the Laplace-transformed correlation functions, which determine the positional and orientational correlation lengths. As density increases, the system exhibits a continuous crossover from a weakly ordered regime with a unimodal orientational distribution to a strongly constrained regime characterized by bimodal orientational ordering. This crossover is accompanied by a nonmonotonic behavior of the pressure relative to the Tonks gas and by a qualitative change in the decay of correlation functions from oscillatory to monotonic. In the high-pressure limit, we show that orientational and positional fluctuations contribute equally to the pressure, leading to a universal ratio of twice the Tonks pressure. The theoretical predictions are supported by numerical solutions of the discretized transfer operator and by scaling arguments that elucidate the high-pressure behavior of ordering and correlation lengths.

cond-mat.soft↗

arXiv2026

Orientational ordering and close packing properties of quasi-one-dimensional hard Gaussian overlap particles

We investigate the orientational ordering and close-packing behavior of hard Gaussian overlap (HGO) particles, which are confined into a quasi-one-dimensional (q1D) channel. In the channel, particles are allowed to move along the channel and to rotate in three dimensions. Using the transfer operator method, we show that oblate particles align with their short axes along the channel, while prolate particles favor planar alignment perpendicular to the axis of the channel. While perfect orientational ordering develops in the fluid of oblate particles, the ordering is just partial in the fluid of prolate ones even at the close-packing density. The pressure ratio of freely rotating and parallel particles (P / P_parallel), which is an effective marker of structural changes, exhibits a single peak for oblate particles and no peak for prolate ones with increasing density. The close-packing behavior is characterized by exponents for the divergence of pressure (P ~ alpha P_parallel), the decay of orientational fluctuations (<(theta_p - theta)^2> ~ P^beta), and the behavior of the orientational correlation length (xi ~ P^gamma). The obtained values are beta = -1 and gamma = 0 for both oblate and prolate particles, while alpha = 2 for oblate and alpha = 1.5 for prolate particles. Moreover, prolate particles belong to the universality class of hard superellipses, where the combinations alpha + beta = 1/2 and beta + gamma = -1 hold exactly for any k > 1 (S. Mizani et al., Phys. Rev. E 111, 064121 (2025)). However, oblate particles do not belong to this universal class because alpha + beta = 1.

cond-mat.soft↗

arXiv2025

Emergence of mixed orientational ordering in quasi-one-dimensional superdisk and superball fluids

We report the discovery of a mixed orientational structure in the quasi-one-dimensional fluid of hard non-spherical bodies with the exact calculation of the thermodynamic and structural quantities using the transfer operator method. The mixed arrangement, which is spatially uniform, but orientionally ordered, cannot be identified with conventional mesophases such as tetratic, cubatic and nematic. It is found that the particles form a mixed orientational arrangement with preferred parallel and perpendicular orientations in a channel, where the number of parallel and perpendicularly oriented particles is not equal even at the close packing density. The mixed structure can be stabilized with hard bodies having equal side lengths in parallel and perpendicular orientations along the channel. These conditions can be realized with colloidal superdisks (superballs) if the curvature of neighboring sides (faces) are different. We show that even a small stretching of the superparticle destabilizes mixed ordering due to perfect nematic order evolving upon approaching close-packing.

cond-mat.soft↗

arXiv2025

Competition between shape anisotropy and deformation in the ordering and close packing properties of quasi-one-dimensional hard superellipse fluids

We investigate the orientational ordering and close-packing behavior of a quasi-one-dimensional (q1D) system of hard superellipses, where the centers of the particles are confined to a line, but they can rotate freely within a two-dimensional plane. The particle shape is tuned between an ellipse and a rectangle by varying the deformation parameter (n). The elongation of the particle is changed using the aspect ratio (k). The pressure ratio between freely rotating and parallel hard superellipses, which displays a single peak, serves as an effective marker for the continuous structural change from quasi-isotropic to nematic ordering. Our findings reveal a competition between the parameters k and n, with k promoting nematic alignment and n favoring tetratic ordering. Notably, in the close-packing regime, the packing properties become independent of k, as the relevant exponents depend solely on n. Furthermore, certain combinations of these exponents exhibit universality, remaining invariant with respect to particle shape

cond-mat.soft↗

arXiv2025

Ordering and association of patchy particles in quasi-one-dimensional channel

We show that the formalism of Wertheim's first order thermodynamic perturbation theory can be generalised for the fluid of rotating sticky particles with anisotropic hard core confined to a quasi-one-dimensional channel. Using the transfer matrix method, we prove that the theory is exact if the hard body interaction is additive, only the first neighbors interact and the particles can stick together only along the channel. We show that the most convenient treatment of association in narrow channels is to work in NPT ensemble, where all structural and thermodynamic quantities can be expressed as a function of pressure and fraction of sites unbonded.

cond-mat.stat-mech↗

arXiv2024

Universality of the close packing properties and markers of isotropic-to-tetratic crossover in quasi-one-dimensional superdisk fluid

We study equilibrium states and ordering regimes of a quasi-one-dimensional system of hard superdisks (anisotropic particles interpolating between disks and squares) where the centers of the particles are constrained to move on a line. A continuous change from a quasi-isotropic to a tetratic regime is found upon increasing the density. Somewhat unexpected, for isobaric states, systems with larger and more anisotropic particles in the tetratic regime are denser than systems with smaller and less anisotropic particles in a quasi-isotropic regime. Close packing behaviour is characterised by exponents describing the behaviour of the pressure, the angular fluctuations and the angular correlation length. We obtain two universal, shape-independent relations between them.

cond-mat.soft↗

arXiv2023

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons--Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.

cond-mat.soft↗

arXiv2020

Three-step melting of hard superdisks in two dimensions

We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual-shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a $D_2$ local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.

cond-mat.soft↗

arXiv2020

Demixing and tetratic ordering in some binary mixtures of hard superellipses

We examine the fluid phase behaviour of the binary mixture of hard superellipses using the scaled particle theory The superellipse is a general two dimensional convex object which can be tuned between circular and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic nematic and tetratic phases even if the aspect ratios of both species are fixed. While the isotropic isotropic demixing transition can be ruled out using the scaled particle theory the first order isotropic nematic and the nematic nematic demixing transition can be stabilized with strong fractionation between the components. It is observed that the demixing tendency is strongest in small rectangle large ellipse mixtures. Interestingly, it is possible to stabilize the tetratic order at lower densities in the mixture of hard squares and rectangles where the long rectangles form nematic phase, while the squares stay in tetratic order.

cond-mat.soft↗

arXiv2019

Orientational ordering and layering of hard plates in narrow slit-like pores

We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with perpendicular one can be detected at high densities. In addition to this, the edge-on monolayer is usually biaxial nematic and a uniaxial-biaxial nematic phase transition can be also seen at very high densities.

cond-mat.soft↗

arXiv2018

Biaxial layering transition of hard rod-like particles in narrow slit-like pores

The phase behavior of hard rectangular rods with length L and diameter D is studied in a narrow slit-like pore using the Parsons-Lee density functional theory. Using the restricted orientation approximation, we find strong adsorption at the walls with planar ordering, second order uniaxial-biaxial ordering transitions and first order layering transitions. The layering transition takes place between two fluids having n and n+1 layers, where the layer spacing is in the order of D. In the case of weak shape anisotropy (L/D=3), the coexisting fluids can be either uniaxial or biaxial, while both phases are found to be biaxial for L/D=6 and L/D=9. Interestingly, even two or more layering transitions can be observed with increasing density at a given shape anisotropy and pore width.

cond-mat.soft↗

arXiv2018

Positional ordering of hard adsorbate particles in tubular nanopores

The phase behaviour and structural properties of a monolayer of hard particles is examined in such a confinement, where the adsorbed particles are constrained to the surface of a narrow hard cylindrical pore. The diameter of the pore is chosen such that only first and second neighbour interactions occur between the hard particles. The transfer operator method of Percus and Zhang [Mol. Phys., 69, 347 (1990)] is reformulated to obtain information about the structure of the monolayer. We have found that a true phase transition is not possible in the examined range of pore diameters. The monolayer of hard spheres undergoes a structural change from fluid-like order to a zigzag-like solid one with increasing surface density. The case of hard cylinders is different in the sense that a layering takes place continuously between a low density one-row and a high density two-row monolayer. Our results reveal a clear discrepancy with classical density functional theories, which do not distinguish smectic-like ordering in bulk from that in narrow periodic pores.

cond-mat.soft↗

arXiv2017

Ordering transitions of weakly anisotropic hard rods in narrow slit-like pores

The effect of strong confinement on the positional and orientational ordering is examined in a system of hard rectangular rods with length L and diameter D (L>D) using the Parsons-Lee modification of the second virial density functional theory. The rods are nonmesogenic (L/D<3)and confined between two parallel hard walls, where the width of the pore (H) is chosen in such a way that both planar (particle's long axis parallel to the walls) and homeotropic (particle's long axis perpendicular to the walls) orderings are possible and a maximum of two layers are allowed to form in the pore. In the extreme confinement limit of ,where only one layer structures appear, we observe a structural transition from a planar to a homeotropic fluid layer with increasing density, which becomes sharper as L->H. In wider pores (2D<H<3D) planar order with two layers, homeotropic order, and even combined bilayer structures (one layer is homeotropic, while the other is planar) can be stabilized at high densities. Moreover, first order phase transitions can be seen between different structures. One of them emerges between a monolayer and a bilayer with planar orders at relatively low packing fractions.

cond-mat.soft↗

arXiv2017

Critical behavior of hard squares in strong confinement

We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length $σ$, where the particles are confined between two parallel walls and only nearest neighbor interactions occur. As in our previous work (PRE, 94, 050603 (2016)), the transfer operator method is used, but here we impose a restricted orientation and position approximation to yield an analytic description of the physical properties. This allows us to study the parallel fluid-like to zigzag solid-like structural transition, where the compressibility and heat capacity peaks sharpen and get higher as $H \rightarrow H_c=2\sqrt{2}-1\approx 1.8284$ and $p \rightarrow p_c= \infty$. Here $H$ is the width of the channel measured in $σ$ units and $p$ is the pressure. We have found that this structural change becomes critical at the $(p_c,H_c)$ point. The obtained critical exponents belong to the universality class of the one-dimensional Ising model. We believe this behavior holds for the unrestricted orientational and positional case.

cond-mat.stat-mech↗

arXiv2017

Ordering of hard rectangles in strong confinement

Using transfer operator and fundamental measure theories, we examine the structural and thermodynamic properties of hard rectangles confined between two parallel hard walls. The side lengths of the rectangle ($L$ and $D$, $L>D$) and the pore width ($H$) are chosen such that maximum two layers are allowed to form in planar order ($L$ is parallel to the wall), while only one in homeotropic order ($D$ is parallel to the wall). We observe three different structures: (i) a low density fluid phase with parallel alignment to the wall, (ii) an intermediate and high density fluid phase with two layers and planar ordering and (iii) a dense single fluid layer with homeotropic ordering. The appearance of these phases and the change in the ordering direction with density is a consequence of the varying close packing structures with $L$ and $H$. Interestingly, even three different structures can be observed with increasing density if $L$ is close to $H$.

cond-mat.soft↗

arXiv2016

Tracking three-phase coexistences in binary mixtures of hard plates and spheres

The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter $σ$) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be preempted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios ($σ$/D) and aspect ratios (L/D). At intermediate values of $σ$/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail for the description of isotropic-isotropic one (Chen et. al., Soft Matter, 11, 5775 (2015)).

cond-mat.soft↗