# Field Induced Memory Effects in Random Nematics

Authors: Amid Ranjkesh; Milan Ambrožič; Samo Kralj; T. J. Sluckin
Journal: Advances in Condensed Matter Physics
 (2014)

---

## Abstract

We studied numerically external field induced memory effects in randomly perturbed nematic liquid crystals. Random anisotropy nematic-type lattice model was used. Theimpurities imposing orientational disorder were randomly spatially distributed with the concentration p below the percolation threshold. Simulations were carried for finite temperatures, where we varied p, interaction strength between LC molecules, and impurities and external field B. In the {
B
,
T
} plane we determined lines separating short range—quasi long range and quasi long range—long range order. Furthermore, crossover regime separating external field and random field dominated regime was estimated. We calculated remanent nematic ordering in samples at B
=
0 as a function of the previously experienced external field strength B.


---

## Body

## 1. Introduction

Impact of weak disorder on statistical properties in phases exhibiting continuous symmetry breaking is of interest for different branches in physics [1–3]. Such systems are of particular interest due to memory effects which they can exhibit [2, 4, 5]. Pioneering studies have been done in magnetic systems [1, 6]. Lately it has been shown that various liquid crystal (LC) phases are extremely adequate for such studies [7]. Namely, LCs are relatively easily experimentally accessible, they display rich diversity of different configurations, and there exists plenty of different means how qualitatively different types of disorder could be imposed to LCs. Consequently, LCs are ideal testing ground to investigate fundamental problems related to impact of weak disorder on phases reached via a symmetry breaking phase transition. In addition, randomly perturbed LCs are also technologically relevant, specially due to their unique combination of liquid character, softness, and optical anisotropy. Randomly perturbed LCs could be exploited for various devices, particularly related to electrooptic applications.Uniaxial nematic phase represents the simplest LC configuration exhibiting only orientational ordering [8]. At mesoscopic level this ordering is commonly described by the nematic director field n
→ and the scalar nematic order parameter S [8]. The unit pseudovector n
→ points along local average uniaxial LC orientational ordering, exhibiting head-to-tail symmetry (i.e., states ±
n
→ are physically equivalent). On the other hand S measures extent of fluctuations about n
→. Absence of thermal fluctuations in local orientational order are fingerprinted in S
=
1. In bulk equilibrium nematic phase is spatially homogeneous where n
→ is aligned along a single symmetry direction. In thermotropic LCs, to which we restrict our study to, nematic long range ordering (LRO) is obtained via the first-order phase transition from the isotropic phase, by decreasing temperature. The latter phase corresponds to ordinary liquid ordering, where S
=
0.There are several different ways how random-type disorder could be experimentally imposed to LCs [7]. For such purposes LCs are either immersed in various porous materials (e.g., aerogels, Vycor glasses, Russian glasses, controlled pore glasses, and millipore membranes…) or by mixing them with different nanoparticles. In the latter case aerosil nanoparticles are commonly used [9]. Namely, by changing their concentration, three qualitatively different types of disorders could be realized [10].Resulting randomly perturbed nematic structures depend on disorder strength. According to the Imry-Ma theorem [1, 6], one expects that weak random field-type disorder stabilizes a domain-type pattern characterized by a single length ξ
d obeying the scaling law ξ
d
~
D
-
2
/
(
4
-
d
). Here D stands for the disorder strength and d is the space dimensionality. The resulting phase should possess short range order (SRO). However, several subsequent studies suggest that the quasi long range order (QLRO) or even LRO might be established [2] instead.In general, randomly perturbed nematic structures possessing SRO or QLRO exhibit glassy features [2]. Namely, strong enough disorder could stabilize enormous large variety of different metastable structures in free energy landscape. Recent experimental and simulation studies in different randomly perturbed nematics support this expectation [4, 9, 11–13]. For example, in LC-aerosil mixtures, it was demonstrated that LCs could memorize external electric or magnetic field induced orientation [4, 5, 14, 15]. Note that systems exposed to relatively strong disorder are known to exhibit several universalities, independent of systems’ microscopic details [2]. However, in case of relatively weak disorder system, specific details are expected to emerge, which further increases diversity of potentially possible phenomena. In addition, glassy features in nematics could be apparently different with respect to magnetic analogues due to nematic head-to-tail symmetry, which is not observed in magnetism. Consequently, perturbed nematics structures in general display complex tangles of topologically stable line disclinations characterized by winding number m
=
-
1
/
2 [5]. On the contrary, line defects could not be topologically stabilized in magnetic systems. Namely, local magnetization could exhibit only line defects with winding number m
=
1, which could avoid singularity in orientational ordering by escaping in “third dimension.” Furthermore, in LCs, thermal fluctuations play relatively important role due to their soft character. Consequently, energy barriers in free energy landscape could be relatively overcrossed easier with respect to magnetic analogues.In the present paper we study disorder enabled memory effects in randomly perturbed LCs. Of our particular interest is external field driven memorization. Our study is numerical, where we use lattice version of modified Random Anisotropy Nematic model [16–18]. The plan of the paper is as follows. In Section 2 we present the model. In Section 3 results of our simulations are presented. In the last section we summarize results. Some technical details related to numerical method and mesoscopic interpretation of results are collected in two appendices.


## 2. Model and Numerical Approach

We use lattice-type simulations where the cubic simulation box of volumeL
3 contains N
=
(
L
/
a
0
)
3 sites. Lengths L and a
0 represent the characteristic linear size of a system and the shortest distance between adjacent lattice sites, respectively. Typically, we set L
/
a
0
=
70. Nematic LC orientational order at each lattice site is presented by the unit vector s
→
i, to which we henceforth refer to as anematic spin. The so-called head-to-tail symmetry ±
s
→
i is considered to mimic typical nematic LC behavior at the mesoscopic level. In addition, we suppose that each site might be populated by a rod-like object with probability p. Their local quenched orientations e
→
i are determined randomly, exhibiting isotropic orientational distribution, where the head-to-tail symmetry and e
→
i
=
1 are imposed. We refer to these pseudovectors asimpurity spins. Note that sites occupied byimpurities are not accessible tonematic spins.Using random number generator we first set static impurity positions and their orientations. For such initial configurations we then determinefixed point configurations ofnematic spins, corresponding to metastable or globally stable structures.


### 2.1. Hamiltonian

The interactions within a system are described by the following Hamiltonian [5, 11, 19, 20]:
(1)
H
=
-
1
2
∑
i
,
j
J
i
j
s
→
i
·
s
→
j
2
-
B
2
∑
i
s
→
i
·
e
⃑

B
2
-
1
2
∑
i
W
i
j
s
→
j
·
e
⃑

i
2
.
The first part of (1) describes short range interaction amongnematic spins, where J
i
j
=
J
>
0 for neighboringspins (each site has 6 first neighbors) and otherwise J
i
j
=
0. The factor 1
/
2 is added in order to avoid double counting of pair-interaction contributions. The second term takes into account presence of a global uniform field B
→
=
B
e
→
B, which we align along the x-axis of the Cartesian coordinate system {
x
,
y
,
z
}. The last term takes into account short range interaction between animpurity at a site i and anematic spin at a site j of strength W
>
0. Therefore, ifimpurity is not present at a site i then W
i
j
=
0. For such choice of interactions anematic spin tends to be oriented parallel to a neighboringnematic orimpurity spin. Furthermore, a finite external field tends to alignnematic spins parallel to its direction. A resulting configuration compromises couplings represented by interaction strengths J, B, and W. Simulation details are described in Appendix A.In simulations we use three qualitatively different histories of systems. We imposed either temperature-quenched history (TQH), field-quenched history (FQH), or temperature-annealed history (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. In case of TQH (FQH) we quench system from isotropic initial distribution (homogeneously alignment alongB
→) ofnematic spins. In case of AH we calculate afixed point configuration {
s
→
i
} at a given temperature originating from an initialfixed point nematic structure which was calculated at a slightly different temperature. Simulations were repeated N
rep
~
10 times for a given set of parameters (i.e., W, p, and a chosen initial condition).


### 2.2. Monitored Quantities

From obtainedfixed point configurations we calculate the global order parameter Q
_
(
g
) and local order parameter tensor Q
_
(
l
). They estimate a global and local degree of orientational ordering, respectively. We define them as follows:(2a)
Q
_
(
g
)
=
1
N
∑
i
1
2
s
→
i
⊗
s
→
i
-
I
_
3
,
(2b)
Q
_
(
l
)
=
1
N
∑
i
1
N
n
n
∑
j
1
2
s
→
i
⊗
s
→
j
-
I
_
3
,where the index i runs over the lattice sites occupied bynematic spins, j runs over all the neighbours (their number is N
n
n) of a site i, I
_ is the identity tensor, and ⊗ marks the tensor product. The average local scalar order parameter s is defined as the largest eigenvector of Q
_
(
l
). On the other hand the average global scalar order parameter S is defined as the largest eigenvector of Q
_
(
g
).We further define the orientational two-point correlation function as [11]:
(3)
G
r
=
3
s
→
i
r
→
i
·
s
→
j
r
→
i
+
r
→
i
j
2
-
1
2
,
where ⋯ is the statistical average of the scalar products ofnematic spin pairs separated by a distance r
=
r
→
i
j
=
r
→
i
-
r
→
j. In case of short range order (SRO) or quasi long range order (QLRO), it holds G
(
r
→
∞
)
→
0. In case of long range order (LRO), it follows G
(
r
→
∞
)
→
G
∞
~
S
2. In general, one expects an exponential decay towards a saturated value of G
(
r
) on increasing r for both LRO and SRO. On the other hand, for QLRO, algebraic decay of correlations is expected; that is, G
(
r
)
∝
r
-
α.In order to obtain structural details fromG
(
r
) for a finite system the correlation function is fitted using the empirical ansatz [11]:
(4)
G
1
r
=
a
e
-
k
r
r
α
+
b
,
where a, b, k, and α are adjustable parameters. The quantity k estimates an average linear size ξ
=
1
/
k of relatively well-correlated regions, referred to asdomains.Note that, in case of QLRO, the decay of correlations with distance is relatively weak, and finite-size effects are expected to be important. Consequently, the power law coefficientα determining algebraic decay of correlations is estimated by the following equation [11, 21, 22]:
(5)
S
∝
L
-
β
,
where β
~
α
/
2, see (4). In case of SRO and LRO, one expects β
~
3
/
2 and β
~
0, respectively, and QLRO is fingerprinted by 0
<
β
<
3
/
2 [11, 23].


## 2.1. Hamiltonian

The interactions within a system are described by the following Hamiltonian [5, 11, 19, 20]:
(1)
H
=
-
1
2
∑
i
,
j
J
i
j
s
→
i
·
s
→
j
2
-
B
2
∑
i
s
→
i
·
e
⃑

B
2
-
1
2
∑
i
W
i
j
s
→
j
·
e
⃑

i
2
.
The first part of (1) describes short range interaction amongnematic spins, where J
i
j
=
J
>
0 for neighboringspins (each site has 6 first neighbors) and otherwise J
i
j
=
0. The factor 1
/
2 is added in order to avoid double counting of pair-interaction contributions. The second term takes into account presence of a global uniform field B
→
=
B
e
→
B, which we align along the x-axis of the Cartesian coordinate system {
x
,
y
,
z
}. The last term takes into account short range interaction between animpurity at a site i and anematic spin at a site j of strength W
>
0. Therefore, ifimpurity is not present at a site i then W
i
j
=
0. For such choice of interactions anematic spin tends to be oriented parallel to a neighboringnematic orimpurity spin. Furthermore, a finite external field tends to alignnematic spins parallel to its direction. A resulting configuration compromises couplings represented by interaction strengths J, B, and W. Simulation details are described in Appendix A.In simulations we use three qualitatively different histories of systems. We imposed either temperature-quenched history (TQH), field-quenched history (FQH), or temperature-annealed history (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. In case of TQH (FQH) we quench system from isotropic initial distribution (homogeneously alignment alongB
→) ofnematic spins. In case of AH we calculate afixed point configuration {
s
→
i
} at a given temperature originating from an initialfixed point nematic structure which was calculated at a slightly different temperature. Simulations were repeated N
rep
~
10 times for a given set of parameters (i.e., W, p, and a chosen initial condition).


## 2.2. Monitored Quantities

From obtainedfixed point configurations we calculate the global order parameter Q
_
(
g
) and local order parameter tensor Q
_
(
l
). They estimate a global and local degree of orientational ordering, respectively. We define them as follows:(2a)
Q
_
(
g
)
=
1
N
∑
i
1
2
s
→
i
⊗
s
→
i
-
I
_
3
,
(2b)
Q
_
(
l
)
=
1
N
∑
i
1
N
n
n
∑
j
1
2
s
→
i
⊗
s
→
j
-
I
_
3
,where the index i runs over the lattice sites occupied bynematic spins, j runs over all the neighbours (their number is N
n
n) of a site i, I
_ is the identity tensor, and ⊗ marks the tensor product. The average local scalar order parameter s is defined as the largest eigenvector of Q
_
(
l
). On the other hand the average global scalar order parameter S is defined as the largest eigenvector of Q
_
(
g
).We further define the orientational two-point correlation function as [11]:
(3)
G
r
=
3
s
→
i
r
→
i
·
s
→
j
r
→
i
+
r
→
i
j
2
-
1
2
,
where ⋯ is the statistical average of the scalar products ofnematic spin pairs separated by a distance r
=
r
→
i
j
=
r
→
i
-
r
→
j. In case of short range order (SRO) or quasi long range order (QLRO), it holds G
(
r
→
∞
)
→
0. In case of long range order (LRO), it follows G
(
r
→
∞
)
→
G
∞
~
S
2. In general, one expects an exponential decay towards a saturated value of G
(
r
) on increasing r for both LRO and SRO. On the other hand, for QLRO, algebraic decay of correlations is expected; that is, G
(
r
)
∝
r
-
α.In order to obtain structural details fromG
(
r
) for a finite system the correlation function is fitted using the empirical ansatz [11]:
(4)
G
1
r
=
a
e
-
k
r
r
α
+
b
,
where a, b, k, and α are adjustable parameters. The quantity k estimates an average linear size ξ
=
1
/
k of relatively well-correlated regions, referred to asdomains.Note that, in case of QLRO, the decay of correlations with distance is relatively weak, and finite-size effects are expected to be important. Consequently, the power law coefficientα determining algebraic decay of correlations is estimated by the following equation [11, 21, 22]:
(5)
S
∝
L
-
β
,
where β
~
α
/
2, see (4). In case of SRO and LRO, one expects β
~
3
/
2 and β
~
0, respectively, and QLRO is fingerprinted by 0
<
β
<
3
/
2 [11, 23].


## 3. Results

We calculatedfixed point configurations ofnematic spins on varying parameters {
W
,
p
,
T
,
B
} andhistories of systems in three-dimensional systems. We limited to concentrations ofimpurities below the percolation threshold, corresponding to the critical concentration p
c
~
0.3 [14]. Of particular interest is impact of external field B on degree of ordering and memory effects.In Figure1 we plot a typical temperature evolution of average degree of ordering s
(
T
) in a temperature loop using AH absence of external field. We started simulations at a relatively high temperature T
=
T
i
>
T
IN, wherenematic spins exhibit essentially isotropic ordering. Here T
IN marks the isotropic-nematic phase transition temperature of a bulk sample. In our simulations we obtain T
IN
~
1.21 which is in line with existing simulation results using similar modelling [11]. Then we were gradually decreasing temperature until the temperature T
f
=
0.5 was reached, corresponding to conditions deep in the nematic phase. Afterwards, we were gradually increasing temperature till T
=
T
i. The plot s
(
T
) reveals that, for example, for {
W
,
p
}
=
{
0.25,0.1
}, the system displays thermal hysteresis, suggesting first-order phase transition. Therefore, the effective disorder imposed by impurities is below the critical value (see Appendix B), above which the first-order phase transition between isotropic (or paranematic) and nematic phase is replaced by a gradual evolution of ordering on varying temperature. Furthermore, one sees that, for {
W
,
p
}
=
{
1,0.1
}, the hysteresis is almost totally suppressed indicating gradual evolution of nematic ordering on varying temperature [17]. Therefore, for this choice of parameters, the effective disorder is supercritical.Temperature evolution of the degree of nematic ordering on decreasing and decreasing temperature. (a)s
(
T
) and (b) Δ
s
=
s
(
up
)
-
s
(
down
), where s
(
up
) and s
(
down
) refer to nematic ordering obtained on increasing and decreasing temperature, respectively. p
=
0.1 and N
=
70.
(a)
(b)Next, we consider impact ofB on nematic ordering. We first demonstrate impact of B on range of ordering. In Figure 2, we plot G
(
r
) dependencies using parameter set {
p
,
W
,
T
}
=
{
0.1,3
,
0.5
}, for (i) B
=
0, (ii) B
=
0.5, and (iii) B
=
0.5 and both histories FQH and TQH. The parameter set {
p
,
W
,
T
} was chosen in such a way that SRO is realized for (i) B
=
0. In the case (ii) the external field is strong enough to replace SRO with QLRO. For still stronger fields, see (iii); LRO is realized. The range of order was obtained via finite size analysis, using (5). For example, in Figure 3(a), we show the finite size analysis for TQH. For (i) B
=
0 (Figure 3(a)), we obtain γ
=
1.54
±
0.05 fingerprinting SRO. For (ii) B
=
0.5, (Figure 3(b)) simulations yield γ
=
0.34
±
0.05, suggesting QLRO. On the other hand for (iii) B
=
1.5, we get γ
=
0.00
±
0.02, indicating LRO (Figure 3(c)). In Table 1 we summarize simulation results for γ on varying B for extreme histories TQH and FQH.Table 1
Finite size analysis data obtained from (A.2). Values of γ reveal range of order within nematic structures. We used different histories of samples (FQH and TQH) and different values of the external field B. Values γ
=
0, 0
<
γ
<
1.5, and γ
=
1.5 reveal LRO, QLRO, and SRO, respectively. W
=
3, p
=
0.1, and T
=
0.5.
B
0
0.5
1
2
TQH
γ = 1.54 ± 0.05
γ = 0.34 ± 0.05
γ = 0.08 ± 0.07
γ = 0.0 ± 0.02
FQH
γ = 1.51 ± 0.08
γ = 0.23 ± 0.08
γ = 0.03 ± 0.04
γ = 0.0 ± 0.01Variation ofG
(
r
) as a function of temperature T for (a) FQH and (b) TQH. p
=
0.1, W
=
3, T
=
0.5, and L
=
70.
(a)
(b)Finite size analysis of structures for TQH using different external field strengths. In all figures we usedp
=
0.1, W
=
3, T
=
0.5, and L
=
70. (a) SRO: γ
=
1.54
±
0.05 and B
=
0; (b) QLRO: γ
=
0.34
±
0.05 and B
=
0.5; (c) LRO: γ
=
0.0
±
0.02 and B
=
1.5.
(a)
(b)
(c)Next, we consider impact ofB on characteristic linear length ξ of the system. The following behavior is expected. For relatively weak external field strengths, theimpurity imposed disorder dominantly influences nematic structure. According to Larkin-Imry-Ma theorem one expects a domain pattern characterized by ξ
d
~
D
-
2
/
(
4
-
d
), where D measures the disorder strength. Our mean-field estimate shown in Appendix B suggests D
∝
W
p (see (B.6)). On the contrary, for relatively large external fields, one expects that the external field coherence length ξ
B
∝
1
/
B characterizing the impact of B in bulk LC system would be observed. Using our simulations we estimate ξ by fitting G
(
r
) dependences, calculated fromfixed point configurations, with (4), where ξ
~
1
/
k. Characteristic dependencies ξ
(
B
) are shown in Figure 4. One indeed observes tendency ξ
~
ξ
B
∝
1
/
B (ξ
~
ξ
d, roughly independent of B) for relatively strong (weak) external field B. We refer to regimes where ξ
~
ξ
B and ξ
~
ξ
d areexternal field dominated regime anddisorder dominated regime, respectively. We estimate crossover values B
=
B
c, which roughly separate both regimes, via intersection of linearized ξ
(
B
) dependencies obtained in limiting regimes B
~
0 and B
≫
10.The characteristic lengthξ as a function of B for (a) W
=
1 and (b) W
=
3. In both figures p
=
0.1, T
=
0.5, and L
=
70.
(a)
(b)Different regimes are indicated in Figure5 in the {
B
,
T
} plane for the parameter set {
W
,
p
}
=
{
3,0.1
}. Here full symbols refer to FQH and empty symbols to TQH. Squares (triangles) indicate the line separating SRO-QLRO (QLRO-LRO) regimes. On the other hand spheres indicate crossover regime separating external field and disorder dominated regime. We determine the respective crossover fields by B
c
(
QLRO
), B
c, and B
c
(
LRO
), corresponding to SRO-QLRO transition, disorder-external field dominance crossover, and QLRO-LRO transition, respectively. With increasing temperature these lines are pushed towards larger values of B. Namely, due to increased thermal fluctuations, higher external fields are needed to reach regime exhibiting qualitatively stronger degree of ordering.Figure 5
Regimes exhibiting different degree of ordering. Squares indicate the SRO-QLRO and triangles the QLRO-LRO transition line. Spheres indicates crossover between disorder and external field dominated regime. FQH: full symbol and TQH: empty symbols.p
=
0.1 and W
=
3.Finally, we analyzed external field controlled memory effects in systems. We performed the followingB-loops. (i) Initial configurations were obtained for a given parameter set {
p
,
W
,
T
} via TQH for B
=
0. (ii) Then we switched on the external field of strength B, for which we calculated afixed point configuration. (iii) Afterwards we switched the field off and calculated the correspondingfixed point nematic structure. We refer to respective configurations as the (i)reference, (ii)field-on, and (iii)field-off structures, respectively. In Figure 6, we plot the average degree of orientational order S obtained from Q
_
(
g
) on increasing B for different anchoring strengths deep in the nematic phase for W
=
3. For this anchoring strength thereference structures exhibit SRO, yielding S
=
0 within numerical error. One sees that infield-on state the degree of ordering is substantially enhanced due to external field induced preference alignment. Infield-off structures finite degree of ordering is preserved providing P
<
0.2. We refer to the resulting ordering asremanent order
S
r. In Figure 6 one sees that S
r
(
B
) displays two different regimes. In theweak field regime
S
r
(
B
) monotonously increases with B until the saturation regime is entered, in which S
r
(
B
) variations are relatively small on varying B.Figure 6
Average degree of ordering for switched-on and afterwards switched-off external ordering fieldB for different values of p. Full symbols: B is switched on. Empty symbols: B is switched off. TQH, W
=
3, T
=
05, and L
=
70.


## 4. Conclusions

We study numerically memory effects using modified Random Anisotropy Nematic-type lattice model [16, 17]. In our modelimpurities are randomly spatially distributed enforcing to nearbynematic spins quenched randomly chosen orientation. In simulations we varied concentration p of impurities, coupling strength W betweennematic spins andimpurities, temperature, and external field strength B. Furthermore, in most simulations we used two extreme histories ofnematic spins, namely, field quenched history (FQH) and temperature quenched history (TQH). Using them, we gain information on memory capabilities of systems of interest. We calculatedfixed point nematic configurations, revealing interplay between nematic interactions, local disordering, and global ordering fields. Fromfixed point configurations we calculated two-point orientational correlation function G
(
r
) and average local and global nematic order parameter. From calculated G
(
r
) profiles we determined characteristic length ξ of the system. Furthermore, using finite size analysis, we determine range of orientational ordering for a given set of parameters.Key results of our study are as follows. We determined regimes exhibiting LRO, QLRO, or SRO orders as a function of temperature and external ordering fieldB. The range of order was determined from values of γ using finite size analysis. Note that the Lakrin-Imry-Ma [1, 6] theorem predicts SRO in absence of B. The theorem was derived for random-field type disorder. However, we used slightly different type of disorder, which is closer to random-bond type imposed frustrations. In simulations we obtained SRO only for strong enough disorder. Furthermore, our simulations confirm that range of order strongly depends on history of samples. In particular, we demonstrate that strong enough applied field B could change range of order. In the {
B
,
T
} plane we estimate critical line separating SRO-QLRO and QLRO-LRO for different histories of samples. Histories play significant role revealing glass-type properties of the systems. Furthermore, we determined impact of B on characteristic linear correlation length ξ within samples. We distinguish between disorder dominated and external field dominated regime. In the first regime impact of B is negligible. On the other hand in the second regime ξ is roughly proportional with 1
/
B. We roughly determined crossover region separating these regimes for different temperatures. We also study impact of temporarily present field B on remanent average nematic ordering S
r. For this purpose we used parameter for which S
r
=
0 (within numerical order) in the reference state obtained in absence of B. We determined magnitude of S
r as a function of B. Our simulations reveal that S
r monotonously increases with B until saturation region is reached.Displayed memory capabilities could be of use for various external field driven memory devices. Modelled systems mimic to some extent LCs confined to various porous matrices or mixtures of nematic LCs with appropriate nanoparticles (e.g., aerosils). In our future studies we intend to explore in more detail analogies between our model and random magnets and spin glasses.



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*Source: 423693-2014-11-30.xml*